<Text-field style="Heading 1" layout="Heading 1">Introdu\303\247\303\243o</Text-field>

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Cap\303\255tulo 16

An\303\241lise Global de uma Fun\303\247\303\243o

A an\303\241lise de uma curva \303\251 discutida em uma sequ\303\252ncia de quatro cap\303\255tulos. Neste cap\303\255tulo o foco \303\251 sobre a identifica\303\247\303\243o de pontos de extremo global: o mais alto e o mais baixo ponto do gr\303\241fico de uma fun\303\247\303\243o em um dado dom\303\255nio. Por exemplo, o lugar mais alto e o mais baixo, n\303\243o cobertos pela \303\241gua na Terra s\303\243o o Monte Everest (eleva\303\247\303\243o: 8849.8 m) e \303\240s margens do Mar Morto (eleva\303\247\303\243o: -411 m). Transformando da macro escala para a micro escala, a identifica\303\247\303\243o individual de cada pico e de cada vale ser\303\241 discutido no pr\303\263ximo cap\303\255tulo. Estes dois t\303\263picos fornecem as ferramentas para montar e resolver uma grande variedade de problemas aplicados de otimiza\303\247\303\243o. Eles tamb\303\251m fornecem uma abordagem simples para fazer o gr\303\241fico de uma fun\303\247\303\243o identificando todos pontos importantes da curva.

Uma aplica\303\247\303\243o imediata do c\303\241lculo de extremos globais \303\251 identificar uma janela de visualiza\303\247\303\243o apropriada para um gr\303\241fico. Por esta raz\303\243o toda an\303\241lise neste cap\303\255tulo ser\303\241 feita sem o uso de um gr\303\241fico da fun\303\247\303\243o. Ap\303\263s completar a an\303\241lise, ser\303\241 constru\303\255do um gr\303\241fico para confirmar os resultados anal\303\255ticos.

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">\303\215ndice de Termos</Text-field>

Os seguintes termos, neste cap\303\255tulo, t\303\252m conex\303\243o com o Dicion\303\241rio do Maple; para mais informa\303\247\303\265es v\303\241 em Dicion\303\241rio Matem\303\241tico.

valorabsoluto

limitesuperior

intervalo

continuo

coseno

pontocritico

curva

extremidade

derivada

descontinuidade

dominio

pontofinal

avaliar

extremo

fun\303\247\303\243o

minimo

gr\303\241fico

intervalo

hipoteses

infinito

intervalo

m\303\241ximo

minimo

negativo

intervalo

optimiza\303\247\303\243o

origem

periodo

fun\303\247\303\243operi\303\263dica

polinomio

quadratica

linhareal

real

satisfazer

conjunto

seno

pontosingular

solu\303\247\303\243o

resolver

fun\303\247\303\243otrigonom\303\251trica

semlimite

valor

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Inicializa\303\247\303\243o</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUShyZXN0YXJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjhRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiO0YnRj0vJSZmZW5jZUdGPC8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y8LyUqc3ltbWV0cmljR0Y8LyUobGFyZ2VvcEdGPC8lLm1vdmFibGVsaW1pdHNHRjwvJSdhY2NlbnRHRjwvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJ0Y6Rj0=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

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Procedimentos Auxiliares </Text-field>

Inserir o cursor em qualquer lugar no seguinte c\303\263digo Maple, e pressionar a Enter.

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

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"> Extremo Global </Text-field>

Coletivamente, os valores m\303\241ximo e m\303\255nimo de um conjunto de valores s\303\243o chamados valores extremos, e da\303\255, o termo extremo. Aproximadamente falando, o ponto mais alto e o mais baixo sobre uma curva s\303\243o seus pontos de extremo global (ou absoluto). A Defini\303\247\303\243o 16.1, a qual faz esta no\303\247\303\243o exata, \303\251 essencialmente uma defini\303\247\303\243o de limite m\303\255nimo superior e limite m\303\241ximo inferior.

Defini\303\247\303\243o 16.1: Extremo Global

Seja f uma fun\303\247\303\243o definida em um conjunto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= .

M \303\251 o valor m\303\241ximo global de f em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn \303\251 o menor n\303\272mero para qual 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 \303\251 v\303\241lido para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn \303\251 valor de m\303\255nimo global de f em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn \303\251 o maior n\303\272mero para o qual 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn \303\251 v\303\241lido para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn.

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Notas</Text-field>

N\303\243o \303\251 necess\303\241rio que os pontos de extremo global sejam valores da fun\303\247\303\243o. (Uma fun\303\247\303\243o n\303\243o tem que conter os seus pontos de extremo global.)

Se permitirmos para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJNRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRKCYjODczNDtGJ0Y0RjdGPkYrRj4= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJtRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYjNiUtRjs2LVEqJnVtaW51czA7RidGPkZARkNGRUZHRklGS0ZNL0ZQUSYwLjBlbUYnL0ZTRlotRiw2JVEoJiM4NzM0O0YnRjRGN0Y+RitGPkYrRj4= ent\303\243o toda fun\303\247\303\243o tem ambos, um m\303\241ximo global e um m\303\255nimo global.

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Ponto 1: Quando os Extremos Globais est\303\243o Inclu\303\255dos entre os Valores da Fun\303\247\303\243o</Text-field>

Um exame cuidadoso das defini\303\247\303\265es de pontos de extremo global revela que n\303\243o \303\251 necess\303\241rio que os valores de extremos sejam valores da fun\303\247\303\243o. De fato, se definimos como sendo o valor m\303\241ximo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJNRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRKCYjODczNDtGJ0Y0RjdGPkYrRj4= para uma fun\303\247\303\243o que n\303\243o seja limitesuperior e o valor m\303\255nimo como sendo 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 para uma fun\303\247\303\243o que n\303\243o seja limitada abaixo, ent\303\243o toda a fun\303\247\303\243o tem os pontos de extremo global. A quest\303\243o mais importante \303\251:

Quando os pontos de extremo global est\303\243o inclu\303\255dos entre os valores da fun\303\247\303\243o em um dado dom\303\255nio? Esta quest\303\243o \303\251 respondida pelo Teorema 16.1.

Teorema 16.1:

Inclus\303\243o dos Extremos Globais

Em um intervalo limitado e fechado LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiYtRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y7USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJiRidGN0Y6RkFGQS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0YrRkE=, a fun\303\247\303\243o cont\303\255nua LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= cont\303\251m seus m\303\241ximos e m\303\255nimos globais.

Um bom modo de compreender este teorema \303\251 olhar todas as maneiras em que a hip\303\263tese pode falhar.

Se a fun\303\247\303\243o n\303\243o \303\251 cont\303\255nua no intervalo fechado 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 , ent\303\243o a fun\303\247\303\243o pode ter ou n\303\243o ter pontos de extremo global.

Se a fun\303\247\303\243o \303\251 cont\303\255nua mas o intervalo n\303\243o \303\251 fechado, ent\303\243o a fun\303\247\303\243o pode ter ou n\303\243o ter pontos de extremo global.

Se a fun\303\247\303\243o \303\251 cont\303\255nua mas o intervalo n\303\243o \303\251 limitado, ent\303\243o a fun\303\247\303\243o pode ter ou n\303\243o ter pontos de extremo global.

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 16.1: Fun\303\247\303\243o Descont\303\255nua em um Intervalo Limitado e<Hyperlink linktarget="Wks:../Dicion\303\241rio/D/discuntinuity.mw" hyperlink="true" encoding="UTF-8">Fechado</Hyperlink></Text-field>

Considere a fun\303\247\303\243o:

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

em um intervalo limitado e fechado LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21vR0YkNi1RIltGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJXRydWVGJy8lKnNlcGFyYXRvckdRJmZhbHNlRicvJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGSi1GIzYmLUkjbW5HRiQ2JFEiMEYnRjUtRjI2LVEiLEYnRjUvRjlGPS9GPEY6L0Y/Rj1GQEZCRkRGRi9GSVEmMC4wZW1GJy9GTFEsMC4zMzMzMzMzZW1GJy1GUDYkUSIyRidGNUY1LUYyNi1RIl1GJ0Y1RjhGO0Y+RkBGQkZERkZGSC9GTFEsMC4xMTExMTExZW1GJ0Y1RitGNQ==. Podemos inser\303\255-la no Maple da forma:

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

LUkqcGllY2V3aXNlRyUqcHJvdGVjdGVkRzYmMkkieEc2IiIiIkYnMUYnIiIjLCYqJiNGKUYrRilGJ0YpRilGLiEiIg==

e o gr\303\241fico, Figura 16.1.

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Figura 16.1

Uma fun\303\247\303\243o descont\303\255nua que n\303\243o cont\303\251m seu ponto de m\303\241ximo global no dom\303\255nio limitado e fechado LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiYtRiM2Ji1JI21uR0YkNiRRIjBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGOC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GNTYkUSIyRidGOEY4RjgvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGK0Y4

Esta fun\303\247\303\243o \303\251 descont\303\255nua em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4=. O menor n\303\272mero com a propriedade tal que 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 para todo x em 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 \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJNRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4=. Como n\303\243o existe nenhum LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= em 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 com 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, esta fun\303\247\303\243o na verdade n\303\243o cont\303\251m seu ponto de m\303\241ximo global em 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. Da mesma forma, o maior n\303\272mero com a propriedade tal que 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 > LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= em 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 \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJtRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4=. Como 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, esta fun\303\247\303\243o cont\303\251m seu ponto de m\303\255nimo globalem 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. (De fato, o m\303\255nimo global est\303\241 contido em ambos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4= .)

Note que quando falamos sobre os pontos de extremo global de uma fun\303\247\303\243o, \303\251 importante enunciar claramente o dom\303\255nio da fun\303\247\303\243oLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=.

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 16.2: <Hyperlink linktarget="Wks:../Dicion\303\241rio/C/continuous.mw" hyperlink="true" encoding="UTF-8">Fun\303\247\303\265es Cont\303\255nuas em Intervalos Abertos</Hyperlink></Text-field>

Considere a fun\303\247\303\243o cont\303\255nua:

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

Ly1JImZHNiI2I0kieEdGJS1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJUYm

no intervalo limitado e 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. Seu gr\303\241fico aparece na Figura 16.2.

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Figura 16.2

Uma fun\303\247\303\243o cont\303\255nua que n\303\243o cont\303\251m seu ponto de m\303\241ximo global no intervalo aberto 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

Sabemos que a fun\303\247\303\243o cosseno \303\251 cont\303\255nua em todo intervalo dos n\303\272meros reais. O 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 \303\251 limitado, por\303\251m aberto. Porque nem LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4= nem 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 est\303\243o no intervalo, esta fun\303\247\303\243o realmente n\303\243o cont\303\251m seu m\303\241ximo global 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. Como 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 = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JS1JI21vR0YkNi1RKiZ1bWludXMwO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZJLUkjbW5HRiQ2JFEiMUYnRjVGNUYrRjU=, a fun\303\247\303\243o cont\303\251m seu m\303\255nimo global no 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.

Note que se qualquer dos valores limites do intervalo estivesse inclu\303\255do no intervalo, ent\303\243o a fun\303\247\303\243o neste exemplo conteria ambos os extremos globais.

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 16.3: Fun\303\247\303\243o Cont\303\255nua em Um Intervalo Ilimitado </Text-field>

Para este exemplo, considere a fun\303\247\303\243o:

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

Ly1JImZHNiI2I0kieEdGJSomLCYiIiJGKiokKUYnIiIjRiohIiJGKiwmRipGKkYrRipGLg==

No intervalo 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. (Tecnicamente, este intervalo \303\251 aberto e fechado ao mesmo tempo.) Figura 16.3 cont\303\251m um gr\303\241fico desta fun\303\247\303\243o.

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Figura 16.3

Uma fun\303\247\303\243o cont\303\255nua que n\303\243o cont\303\251m seu m\303\255nimo global no dom\303\255nio ilimitado LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiQtRiM2Ji1GLDYlUTEmdW1pbnVzMDsmaW5maW47RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y7USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSgmaW5maW47RidGN0Y6RkFGQUYrRkE=

O m\303\241ximo global para esta fun\303\247\303\243o em toda reta real \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJNRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4=; o m\303\255nimo global \303\251LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JS1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSUYrRjVGK0Y1 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. O m\303\241ximo global est\303\241 em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4= mas n\303\243o h\303\241 nenhum n\303\272mero real no qual 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.

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 16.4: Um Exemplo Final</Text-field>

Defina a fun\303\247\303\243o:

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

Ly1JImZHNiI2I0kieEdGJSokKUYnIiIjISIi

para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJm5lO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1JI21uR0YkNiRRIjBGJ0Y+Rj5GK0Y+. Esta fun\303\247\303\243o \303\251 cont\303\255nua em qualquer intervalo que n\303\243o inclua a origem. Em um 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 com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= > LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= > 0, os pontos de extremo global de f em 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 s\303\243o 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 = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JkYrLUYjNiZGKy1JJW1zdXBHRiQ2JS1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvRjlRJ2l0YWxpY0YnLUY1NiRRIjJGJ0Y4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRjhGK0Y4LyUubGluZXRoaWNrbmVzc0dGNy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZULyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGOA== e 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 = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JkYrLUYjNiZGKy1JJW1zdXBHRiQ2JS1GLDYlUSJiRicvJSdpdGFsaWNHUSV0cnVlRicvRjlRJ2l0YWxpY0YnLUY1NiRRIjJGJ0Y4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRjhGK0Y4LyUubGluZXRoaWNrbmVzc0dGNy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZULyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGOA== . A figura 16.6 mostra o gr\303\241fico desta fun\303\247\303\243o em um intervalo \303\240 direita da origem.

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Figura 16.4

Uma fun\303\247\303\243o cont\303\255nua em um intervalo limitado e fechado

Se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= < LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= < 0, ent\303\243o 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 = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JkYrLUYjNiZGKy1JJW1zdXBHRiQ2JS1GLDYlUSJiRicvJSdpdGFsaWNHUSV0cnVlRicvRjlRJ2l0YWxpY0YnLUY1NiRRIjJGJ0Y4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRjhGK0Y4LyUubGluZXRoaWNrbmVzc0dGNy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZULyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGOA== e 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 = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JkYrLUYjNiZGKy1JJW1zdXBHRiQ2JS1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvRjlRJ2l0YWxpY0YnLUY1NiRRIjJGJ0Y4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRjhGK0Y4LyUubGluZXRoaWNrbmVzc0dGNy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZULyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGOA==. A figura 16.5 mostra um gr\303\241fico da fun\303\247\303\243o em um intervalo \303\240 esquerda da origem.

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Figura 16.5

Uma fun\303\247\303\243o cont\303\255nua em um intervalo limitado e fechado

em qualquer um dos casos, se um ou ambos os limites do intervalo forem omitidos, o intervalo n\303\243o ser\303\241 mais um intervalo fechado e o correspondente extremo global n\303\243o estar\303\241 mais contido no intervalo.

A fun\303\247\303\243o \303\251 descont\303\255nua em qualquer intervalo que contenha a origem. Se um dos limites do intervalo for 0 ent\303\243o o m\303\241ximo global neste intervalo ser\303\241 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJNRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRKCYjODczNDtGJ0Y0RjdGPkYrRj4=. Um extremo infinito nunca pode estar contido!

Cada um destes resultados \303\251 consistente com o enunciado do teorema.

<Text-field style="Heading 1" readonly="true" layout="Heading 1">Maple T.A. Maple-Graded Question</Text-field>

Using the Maple-graded question type, you create a question that uses Maple functionality when creating the correct answer and determining if the student's response is correct. The Maple-graded question type has an option to plot the student's response. To include the plot option, insert the corresponding task template. For information on creating questions, making assignments, and exporting Maple T.A. course modules, see Overview of Maple T.A. Integration.

<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>

Algorithmic variables can be used to create a question that contains randomly generated parameters. You can refer to algorithmic variables in the Question, Answer, Hints, and Feedback input regions, as well as in other variable definitions. To reference an algorithmic variable, include "`$variable`" as text or 2-D Math, for example, x := `$myvariable`. Adding algorithmic variables to the question is optional. In the following execution group, add an algorithmic variable. To include more variables, add more execution groups. If your assignment contains more than one algorithmic variable, ensure the variable names are unique.

with(RandomTools): randomize(): fn2 := sort(Generate(polynom(integer(range=-10..10),x,degree=1))): fn3 := sort(Generate(polynom(integer(range=-10..10),x,degree=1))): n4 := Generate(integer(range=1..5)): n5 := Generate(integer(range=2..8)): while (n4 >= n5) do n5 := Generate(integer(range=2..6)) end do: fn4 := piecewise(x < n4,fn2,x>=n4,fn3); #plot(fn4,x=0..n5,discont=true);

LUkqcGllY2V3aXNlRyUqcHJvdGVjdGVkRzYmMkkieEc2IiIiJiwmRichIiQiIigiIiIxRilGJywmRiciIiUiIidGLQ==

ymax2 := max(eval(fn3,x=n4),eval(fn3,x=n5)): if (ymax2 = eval(fn3,x=n4)) then xmax2 := n4: xmin2 := n5: ymin2 := eval(fn3,x=n5): else xmax2 := n5: xmin2 := n4: ymin2 := eval(fn3,x=n4): end if: if (ymax2 < eval(fn2,x=0)) then ymax2 := eval(fn2,x=0): xmax2 := 0: elif (ymin2 > eval(fn2,x=0)) then ymin2 := eval(fn2,x=0): xmin2 :=0: end if: if (ymax2 < eval(fn2,x=n4)) then ans1 := {[xmin2,ymin2,'min']}; elif (ymin2 > eval(fn2,x=n4)) then ans1 := {[xmax2,ymax2,'max']}; else ans1 := {[xmax2,ymax2,'max'],[xmin2,ymin2,'min']}; end if;

PCM3JSIiJyIjSUkkbWF4RyUqcHJvdGVjdGVkRw==

JSFH

<Text-field style="Heading 1" layout="Heading 1">Quest\303\243o 16.1</Text-field>

The question can contain text, 2-D Math, plots, images, and algorithmic variables. To insert a plot in the question, use the Plot Component. In the following text region, enter the full contents of the question.

Considere a fun\303\247\303\243o f(x) = `$fn4` no intervalo [`$n4`,`$n5`]. Encontre o extremo global. Insira sua resposta como {[x-coord, y-coord, tipo], etc.}. Insira o tipo como max ou min.

JSFH

<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>

To evaluate a student's response, enter the correct answer. Complete each line of code with a semicolon. The last line must evaluate to an expression that will be stored as the variable `$ANSWER`. Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed.

JSFHans1;

<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>

To evaluate a student's response, you must evalute to a Boolean value (true or false). The variable `$RESPONSE` is automatically initialized to the student's response. Using `$ANSWER` (the correct answer) and `$RESPONSE` (the student response), one example of evaluating to a Boolean value is, evalb(`$ANSWER`-`$RESPONSE`=0); Enter Maple code to evaluate a student's response. To add additional Maple functionality, use the Answer input region.

evalb(`$ANSWER`=`$RESPONSE`);

<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>

A question can offer hints to students when requested. Hints can contain text, 2-D Math, and algorithmic variables. Adding hints to the question is optional. Enter your hints in the following table. You can provide up to three hints.

Take note of the discontinuity.

Does the function reach a global max/min?

Replace this text with hint 3.

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea1`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Take note of the discontinuity.</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea1`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Does the function reach a global max/min?</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>

A question can display feedback when a student provides an incorrect response. The feedback can contain text, 2-D Math, and algorithmic variables. The feedback can also refer to `$RESPONSE` (the student response) and `$ANSWER` (the correct answer). Adding feedback to the question is optional. In the following text region, enter feedback to an incorrect response.

Replace this text with feedback.

with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea1`, `value`); ANSWER := ans1; if evalb(ANSWER=eval(parse(StudentResponse))) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!&NewLine;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='{' close='}' separators=','><mrow><mfenced open='[' close=']' separators=','><mrow><mn>6</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>30</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>max</mi></mrow></mfenced></mrow></mfenced></mrow></mstyle></math><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>&NewLine;</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='{' close='}' separators=','><mrow><mfenced open='[' close=']' separators=','><mrow><mn>6</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>30</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>max</mi></mrow></mfenced></mrow></mfenced></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;

<Text-field style="Heading 1" readonly="true" layout="Heading 1">Maple T.A. Maple-Graded Question</Text-field>

<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>

with(plots): with(RandomTools): randomize(): r1 := Generate(choose([-10..-1,1..10])): n6 := Generate(integer(range=r1)): n7 := Generate(integer(range=-10..10)): n8 := Generate(integer(range=-5..-1)): n9 := Generate(integer(range=1..10)): while (evalf((n9-n8) < Pi)) do n9 := Generate(integer(range=1..10)) end do: n10 := Generate(choose([1,2,3])): fn5 := sort(Generate(polynom(integer(range=-10..10),x,degree=2))): fn6 := (fn5,n6*sin(x+n7),n6*cos(x+n7))[n10]; interval2 := ``(n8,n9); #plot(fn6,x=n8..n9);

LCQtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmSSJ4R0YoIiIiISIlRiwhIiM=

LUkhRzYiNiQhIiQiIio=

rdfn2 := fsolve(diff(fn6,x)=0,x): if (n10 = 1) then if verify(rdfn2,n8..n9,interval('open')) then temp2 := evalf(eval(diff(fn6,x,x),x=rdfn2)): type2 := `if`(temp2>0,'min','max'); ans2 := {[evalf(rdfn2,4),evalf(eval(fn6,x=rdfn2),4),type2]}; else ans2 := {}; end if; else if (rdfn2 > n9) then temp4 := 0; while (evalb(evalf(n9) < evalf(rdfn2 + (temp4*Pi)))=true) do temp4 := temp4-1; end do; temp3 := temp4; while (evalb(evalf(n8) < evalf(rdfn2 + ((temp3-1)*Pi)))=true) do temp3 := temp3-1; end do; elif (rdfn2 > n8) then temp3 := 0; while (n8 < evalf(rdfn2 + (temp3-1)*Pi)) do temp3 := temp3-1; end do; temp4 := 0; while (n9 > evalf(rdfn2 + (temp4+1)*Pi)) do temp4 := temp4+1; end do; else temp3 := 0; while (n8 > evalf(rdfn2 + temp3*Pi)) do temp3 := temp3+1; end do; temp4 := temp3; while (n9 > evalf(rdfn2 + (temp4+1)*Pi)) do temp4 := temp4+1; end do; end if; if (temp3 = temp4) then temp5 := evalf(rdfn2+Pi*temp3); ans2 := {[evalf(temp5,4),eval(fn6,x=temp5),`if`(eval(fn6,x=temp5)>0,'max','min')]}; else ans2 := {seq([evalf(rdfn2+Pi*i,4),eval(fn6,x=rdfn2+Pi*i),`if`(eval(fn6,x=rdfn2+Pi*i)>0,'max','min')],i=temp3..temp4)}; end if; end if; ans2;

PCY3JSQhJSVHIyEiJCQhIiMiIiFJJG1pbkclKnByb3RlY3RlZEc3JSQiJSVlKSEiJSQiIiNGKUkkbWF4R0YrNyUkIiUrU0YmRidGKjclJCIlVXJGJkYwRjI=

JSFH

<Text-field style="Heading 1" layout="Heading 1">Quest\303\243o 16.2</Text-field>

Considere a fun\303\247\303\243o f(x) = `$fn6` no intervalo `$interval2`. Encontre o extremo global. Insira sua resposta como {[x-coord, y-coord, tipo], etc.}. Insira o tipo como max ou min. Se n\303\243o existem extremos globais, insira sua resposta como {}. Voc\303\252 pode inserir sua resposta com precis\303\243o de 4 d\303\255gitos significativos.

JSFH

<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>

JSFHans2;

<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>

evalb(evalf(`$ANSWER`=`$RESPONSE`,4));

<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>

Are there global extrema within the open interval?

Replace this text with hint 2.

Replace this text with hint 3.

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea2`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Are there global extrema within the open interval?</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>

Replace this text with feedback.

with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea2`, `value`); ANSWER := ans2; if evalb(evalf(ANSWER=eval(parse(StudentResponse)),4)) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!&NewLine;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='{' close='}' separators=','><mrow><mfenced open='[' close=']' separators=','><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>2.284</mn></mrow><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>2.</mn></mrow><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>min</mi></mrow></mfenced><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mfenced open='[' close=']' separators=','><mrow><mn>0.8584</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>2.</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>max</mi></mrow></mfenced><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mfenced open='[' close=']' separators=','><mrow><mn>4.000</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>2.</mn></mrow><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>min</mi></mrow></mfenced><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mfenced open='[' close=']' separators=','><mrow><mn>7.142</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>2.</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>max</mi></mrow></mfenced></mrow></mfenced></mrow></mstyle></math><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>&NewLine;</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='{' close='}' separators=','><mrow><mfenced open='[' close=']' separators=','><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>2.284</mn></mrow><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>2.</mn></mrow><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>min</mi></mrow></mfenced><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mfenced open='[' close=']' separators=','><mrow><mn>0.8584</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>2.</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>max</mi></mrow></mfenced><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mfenced open='[' close=']' separators=','><mrow><mn>4.000</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>2.</mn></mrow><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>min</mi></mrow></mfenced><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mfenced open='[' close=']' separators=','><mrow><mn>7.142</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>2.</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>max</mi></mrow></mfenced></mrow></mfenced></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;

<Text-field style="Heading 1" readonly="true" layout="Heading 1">Maple T.A. Maple-Graded Question</Text-field>

<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>

with(RandomTools): randomize(): n11 := Generate(integer(range=1..10)): n12 := Generate(integer(range=1..10)): n13 := Generate(integer(range=1..10)): #n13 := Generate(integer(range=1..4)): n14 := Generate(integer(range=1..10)): n15 := Generate(integer(range=1..10)): #n16 := Generate(integer(range=1..4))*2: #while (n13 > n16) do n13 := Generate(integer(range=1..4)) end do: fn7 := (n11-n12*x)/(n14+n15*x^2); dfn7 := simplify(diff(fn7,x)); rdfn7 := convert({fsolve(numer(dfn7)=0,x)},list); lmax7 := max(limit(fn7,x=infinity),limit(fn7,x=-infinity)); lmin7 := max(limit(fn7,x=infinity),limit(fn7,x=-infinity)); ymin7 := evalf(lmin7): ymax7 := evalf(lmax7): max7check := false: min7check := false: for k from 1 to nops(rdfn7) do temp6 := eval(diff(fn7,x,x),x=rdfn7[k]); temp7 := eval(fn7,x=rdfn7[k]); if (temp7 < ymin7 and temp7 <> lmin7) then xmin7 := rdfn7[k]; ymin7 := temp7; min7check := true; elif (temp7 > ymax7 and temp7 <> lmax7) then xmax7 := rdfn7[k]; ymax7 := temp7; max7check := true; elif (temp7 = ymin7 and temp7 <> lmin7) then xmin7 := xmin7,rdfn7[k]; ymin7 := ymin7,ymin7; elif (temp7 = ymax7 and temp7 <> lmax7) then xmax7 := xmax7,rdfn7[k]; ymax7 := ymax7,ymax7; end if; end do: if (min7check=true) and (max7check=true) then ans3 := {seq(evalf([[xmin7][ii],[ymin7][ii],'min'],4),ii=1..nops([xmin7])), seq(evalf([[xmax7][jj],[ymax7][jj],'max'],4),jj=1..nops([xmax7]))}; elif (max7check=true) then ans3 := {seq([[xmax7][ii],[ymax7][ii],'max'],ii=1..nops([xmax7]))}; elif (min7check=true) then ans3 := {seq([[xmin7][ii],[ymin7][ii],'min'],ii=1..nops([xmin7]))}; else ans3 := {}; end if; #plot(fn7,x=-20..20,y=ymin7..ymax7);

KiYsJiIiKSIiIkkieEc2IiEjNUYlLCZGJEYlKiRGJiIiIyIiJyEiIg==

KiYsKCEjPyIiIiokSSJ4RzYiIiIjIiM6RichI0NGJSwmIiIlRiVGJiIiJCEiIw==

NyQkIStQJFF2LychIzUkIitNUXYvQSEiKg==

IiIh

PCQ3JSQhJVtnISIlJCIleTghIiRJJG1heEclKnByb3RlY3RlZEc3JSQiJTBBRikkISUheSRGJkkkbWluR0Yr

JSFH

<Text-field style="Heading 1" layout="Heading 1">Quest\303\243o 16.3</Text-field>

Considere a fun\303\247\303\243o f(x) = `$fn7`. Encontre o extremo global em um intervalo ilimitado. Insira sua resposta como {[x-coord, y-coord, tipo], etc.}. Insira tipo como max ou min. Se n\303\243o existem extremos globais, entre sua resposta como {}. Voc\303\252 pode inserir sua resposta com 4 d\303\255gitos significativos.

JSFH

<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>

JSFHans3;

<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>

evalb(evalf(`$ANSWER`=`$RESPONSE`,4));

<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>

What are 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and 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?

Does 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 have global extrema? To find possible extrema, solve 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, and evaluate 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 at those values.

Replace this text with hint 3.

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea3`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>What are </mtext><mstyle fontfamily='serif' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><munder><mo fontfamily='serif' lspace='0.0em' rspace='0.1666667em' movablelimits='true'>lim</mo><mrow><mi>x</mi><mo fontfamily='serif' lspace='0.2777778em' rspace='0.2777778em' stretchy='true'>→</mo><mi>∞</mi></mrow></munder><mo fontfamily='serif' lspace='0.0em' rspace='0.0em'>⁡</mo><mrow><mi>f</mi><mo fontfamily='serif' lspace='0.0em' rspace='0.0em'>⁡</mo><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mrow></mrow></mstyle><mtext>and </mtext><mstyle fontfamily='serif' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><munder><mo fontfamily='serif' lspace='0.0em' rspace='0.1666667em' movablelimits='true'>lim</mo><mrow><mi fontfamily='serif'>x</mi><mo fontfamily='serif' lspace='0.2777778em' rspace='0.2777778em' stretchy='true'>→</mo><mi fontfamily='serif'>&uminus0;∞</mi></mrow></munder><mo fontfamily='serif' lspace='0.0em' rspace='0.0em'>⁡</mo><mrow><mi fontfamily='serif'>f</mi><mo fontfamily='serif' lspace='0.0em' rspace='0.0em'>⁡</mo><mfenced open='(' close=')' separators=','><mrow><mi fontfamily='serif'>x</mi></mrow></mfenced></mrow></mrow></mrow></mstyle><mtext>?</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea3`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Does </mtext><mstyle fontfamily='serif' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mi>f</mi><mo fontfamily='serif' lspace='0.0em' rspace='0.0em'>⁡</mo><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mrow></mstyle><mtext> have global extrema?  To find possible extrema, solve </mtext><mstyle fontfamily='serif' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mo fontfamily='serif' lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mrow><mo fontfamily='serif' lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi fontfamily='serif'>x</mi></mrow></mfrac><mrow><mi>f</mi><mo fontfamily='serif' lspace='0.0em' rspace='0.0em'>⁡</mo><mfenced open='(' close=')' separators=','><mrow><mi fontfamily='serif'>x</mi></mrow></mfenced></mrow><mo fontfamily='serif' lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn fontfamily='serif'>0</mn></mrow></mstyle><mtext>, and evaluate </mtext><mstyle fontfamily='serif' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mi fontfamily='serif'>f</mi><mo fontfamily='serif' lspace='0.0em' rspace='0.0em'>⁡</mo><mfenced open='(' close=')' separators=','><mrow><mi fontfamily='serif'>x</mi></mrow></mfenced></mrow></mrow></mstyle><mtext> at those values.</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>

Replace this text with feedback.

with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea3`, `value`); ANSWER := ans3; if evalb(evalf(ANSWER=eval(parse(StudentResponse)),4)) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!&NewLine;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='{' close='}' separators=','><mrow><mfenced open='[' close=']' separators=','><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>0.6048</mn></mrow><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>1.378</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>max</mi></mrow></mfenced><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mfenced open='[' close=']' separators=','><mrow><mn>2.205</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>0.3780</mn></mrow><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>min</mi></mrow></mfenced></mrow></mfenced></mrow></mstyle></math><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>&NewLine;</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='{' close='}' separators=','><mrow><mfenced open='[' close=']' separators=','><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>0.6048</mn></mrow><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>1.378</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>max</mi></mrow></mfenced><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mfenced open='[' close=']' separators=','><mrow><mn>2.205</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>0.3780</mn></mrow><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>min</mi></mrow></mfenced></mrow></mfenced></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Defini\303\247\303\243o: Pontos Estacion\303\241rios, Singulares e Cr\303\255ticos</Text-field>

A an\303\241lise cont\303\255nua das caracter\303\255sticas dos gr\303\241ficos das fun\303\247\303\265es \303\251 ampliada pela seguinte defini\303\247\303\243o.

Defini\303\247\303\243o 16.2: Pontos Estacion\303\241rios, Singulares, e Cr\303\255ticos

Seja f uma fun\303\247\303\243o definida em um intervalo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= um ponto de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 um ponto singular de f em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSRmfidGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUTAmQXBwbHlGdW5jdGlvbjtGJy9GOFEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUS1GIzYmLUY7Ni1RIihGJ0Y+L0ZBRjZGQy9GRkY2RkdGSUZLRk0vRlBRLDAuMTY2NjY2N2VtRicvRlNGZm4tRiM2JC1GLDYlUSJjRidGNEY3Rj4tRjs2LVEiKUYnRj5GWUZDRlpGR0ZJRktGTUZlbi9GU1EsMC4xMTExMTExZW1GJ0Y+RitGPkYrRj4= n\303\243o existe e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 um ponto interno de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= (Portanto, um ponto singular n\303\243o est\303\241 no limite de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, mas \303\251 um ponto onde o gr\303\241fico da fun\303\247\303\243o tem um salto, uma ass\303\255ntota vertical, um bico ou uma c\303\272spide.)

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 um ponto cr\303\255tico de f em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 um ponto estacion\303\241rio de f em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, ou LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 um ponto singular de f em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, ou LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 um ponto no limite de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Ponto 2: Onde Ocorre um Extremo Global?</Text-field>

Saber quando um ponto de extremo global est\303\241 contido no dom\303\255nio \303\251 importante. Nos exemplos, a identifica\303\247\303\243o dos extremos globais foi baseada na visualiza\303\247\303\243o de um gr\303\241fico da fun\303\247\303\243o em um dom\303\255nio espec\303\255fico. Quanto a um gr\303\241fico poder ser \303\272til na identifica\303\247\303\243o de extremos globais, \303\251 como colocar a carro\303\247a na frente dos bois. O conhecimento sobre extremos globais \303\251 geralmento usado para selecionar a janela de visualiza\303\247\303\243o para o gr\303\241fico. Logo, a real quest\303\243o \303\251:

Como podemos determinar um ponto de extremo global de uma fun\303\247\303\243o cont\303\255nua em um intervalo limitado e fechado sem olhar para um gr\303\241fico ?

Expressamos a resposta desta quest\303\243o no Teorema 16.2:

Teorema 16.2: Localiza\303\247\303\243o de um Extremo Global

Seja f uma fun\303\247\303\243o definida no intervalo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Se um valor extremo de f em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 alcan\303\247ado no ponto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= contido no intervalo, ent\303\243o o ponto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= deve ser um ponto cr\303\255tico de f em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= .

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 16.5: <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> em [ -2, 2 ] </Text-field>

Encontre o(s) ponto(s) de extremo global e sua(s) localiza\303\247\303\243o(\303\265es) para

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

Ly1JImZHNiI2I0kieEdGJSwoKiQpRiciIiQiIiJGLComRitGLClGJyIiI0YsISIiRidGMA==

no intervalo:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEjSTVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSM6PUYnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZTLUkobWZlbmNlZEdGJDYmLUYjNihGKy1GIzYmLUY9Ni1RKiZ1bWludXMwO0YnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yMjIyMjIyZW1GJy9GVUZbby1JI21uR0YkNiRRIjJGJ0ZALyUrZXhlY3V0YWJsZUdGREZALUY9Ni1RIixGJ0ZARkIvRkZGOEZHRklGS0ZNRk8vRlJRJjAuMGVtRicvRlVRLDAuMzMzMzMzM2VtRidGXW9GYW9GQEZALyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmFvRkBGK0Zhb0ZALUY9Ni1RIjpGJ0ZARkJGRUZHRklGS0ZNRk9GUUZURmFvRkA=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUy1GLDYlUSNJNUYnRjZGOS8lK2V4ZWN1dGFibGVHRkRGQEYrRllGQEYrRllGQA==

L14jIiIiNyQhIiMiIiM=

Esta fun\303\247\303\243o \303\251 cont\303\255nua em um intervalo limitado e fechado, de modo que os extremos globais est\303\243o contidos. Acabamos de aprender que os locais poss\303\255veis para os extremos estarem localizados s\303\243o:

o limite do intervalo;

qualquer ponto estacion\303\241rio da fun\303\247\303\243o que esteja no intervalo;

ou qualquer ponto singular localizado no intervalo (mas lembre-se que polin\303\264mios n\303\243o possuem pontos singulares!);

Para este exemplo, n\303\243o existe nenhum ponto singular (pois nenhum polin\303\264mio tem um ponto singular). Inserindo no Maple:

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

Os pontos estacion\303\241rios s\303\243o as solu\303\247\303\265es da equa\303\247\303\243o 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, isto \303\251, de:

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

LywoKiYiIiQiIiIpSSJ4RzYiIiIjRiZGJiomIiInRiZGKEYmISIiRiZGLSIiIQ==

As duas solu\303\247\303\265es para esta equa\303\247\303\243o quadr\303\241tica s\303\243o:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSZzdGF0NUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

NiQsJiIiIkYkKiYjIiIjIiIkRiQpRigjRiRGJ0YkRiQsJkYkRiRGJSEiIg==

Os limites do intervalo s\303\243o:

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

NiQhIiMiIiM=

O conjunto completo de localiza\303\247\303\265es poss\303\255veis para os extremos globais \303\251 formado destas listas com todos os pontos fora do intervalo removidos. A lista de pontos cr\303\255ticos \303\251:

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

NyUhIiMiIiMsJiIiIkYmKiYjRiQiIiRGJilGKSNGJkYkRiYhIiI=

(Note que um dos pontos cr\303\255ticos n\303\243o est\303\241 dentro do intervalo; este n\303\243o ser\303\241 considerado.)

Tudo que resta \303\251 avaliar a fun\303\247\303\243o para cada um destes pontos. Isto leva aos valores:

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

NiU3JCEiIyEjPTckIiIjISInNyQsJiIiIkYrKiYjRiciIiRGKylGLiNGK0YnRishIiIsJkYuRjEqJiMiIzsiIipGK0YvRitGKw==

ou, na forma de ponto flutuante:

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

NiU3JCQhIiMiIiEkISM9RiY3JCQiIiNGJiQhIidGJjckJCEkYiIhIiQkIiN6RjE=

O maior valor da fun\303\247\303\243o \303\251 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 e o menor valor da fun\303\247\303\243o \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GTy9GUlEsMC4xNjY2NjY3ZW1GJy9GVUZobi1GIzYmRistRiM2JS1GPTYtUSomdW1pbnVzMDtGJ0ZARkJGRUZHRklGS0ZNRk9GUUZULUkjbW5HRiQ2JFEiMkYnRkBGQEYrRkAtRj02LVEiKUYnRkBGZW5GRUZmbkZJRktGTUZPRmduL0ZVUSwwLjExMTExMTFlbUYnRkBGK0ZALUY9Ni1RIj1GJ0ZARkJGRUZHRklGS0ZNRk8vRlJRLDAuMjc3Nzc3OGVtRicvRlVGXnAtRiM2JUZeby1GYm82JFEjMThGJ0ZARkBGK0ZARitGQA== , logo o m\303\241ximo global ocorre para o ponto cr\303\255tico 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 e o m\303\255nimo global para o limite esquerdo do intervalo 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. Estes resultados s\303\243o confirmados na Figura 16.6:

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Figura 16.6

Exemplo 16.5: Gr\303\241fico de 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 emLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiYtRiM2Ji1JI21uR0YkNiRRKyZ1bWludXMwOzJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGOC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GNTYkUSIyRidGOEY4RjgvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGK0Y4

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 16.6: <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> em [-1, 3]</Text-field>

Considere a mesma c\303\272bica (polin\303\264mio de grau 3) do Exemplo 16.5, isto \303\251, a regra:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEjZjZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSM6PUYnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZTLUYsNiVRI2Y1RidGNkY5LyUrZXhlY3V0YWJsZUdGREZARitGWUZALUY9Ni1RIjpGJ0ZARkJGRUZHRklGS0ZNRk9GUUZURllGQA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNihGKy1GIzYnLUYsNiVRImZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUTAmQXBwbHlGdW5jdGlvbjtGJy9GPFEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkYvJSlzdHJldGNoeUdGRi8lKnN5bW1ldHJpY0dGRi8lKGxhcmdlb3BHRkYvJS5tb3ZhYmxlbGltaXRzR0ZGLyUnYWNjZW50R0ZGLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGVS1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInhGJ0Y4RjsvJStleGVjdXRhYmxlR0ZGRkJGQkZqbkZCLUY/Ni1RIj1GJ0ZCRkRGR0ZJRktGTUZPRlEvRlRRLDAuMjc3Nzc3OGVtRicvRldGYG8tRiw2JVEjZjZGJ0Y4RjtGam5GQkYrRmpuRkJGK0ZqbkZC

Ly1JImZHNiI2I0kieEdGJSwoKiQpRiciIiQiIiJGLComRitGLClGJyIiI0YsISIiRidGMA==

por\303\251m, que o dom\303\255nio seja agora o intervalo:

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

L14jIiIiNyQhIiIiIiQ=

Esta fun\303\247\303\243o \303\251 cont\303\255nua em um intervalo limitado e fechado tal que ambos os pontos de extremo global est\303\243o contidos. Os poss\303\255veis locais de ocorrer pontos de extremo s\303\243o :

os pontos limites do intervalo:

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

NiQhIiIiIiQ=

quaisquer pontos estacion\303\241rios (as solu\303\247\303\265es de 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 fora do intervalo ser\303\243o exclu\303\255das posteriormente):

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSZzdGF0NkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

NiQsJiIiIkYkKiYjIiIjIiIkRiQpRigjRiRGJ0YkRiQsJkYkRiRGJSEiIg==

ou quaisquer pontos singulares:

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

O conjunto completo de todos os locais poss\303\255veis para pontos de extremo global \303\251 formado destas listas com todos os pontos fora do intervalo removidos.

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

NyYhIiIiIiQsJiIiIkYmKiYjIiIjRiRGJilGJCNGJkYpRiZGJiwmRiZGJkYnRiM=

Tudo que resta \303\251 avaliar a fun\303\247\303\243o em cada um destes pontos, obtendo:

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

NiY3JCEiIiEiJDckIiIkRiU3JCwmIiIiRioqJiMiIiNGJ0YqKUYnI0YqRi1GKkYqLCZGJ0YkKiYjIiM7IiIqRipGLkYqRiQ3JCwmRipGKkYrRiQsJkYnRiRGMUYq

ou, na forma com ponto flutuante:

NiY3JCQhIiIiIiEkISIkRiY3JCQiIiRGJkYnNyQkIiViQEYoJCElemdGKDckJCEkYiJGKCQiI3pGKA==

O maior valor da fun\303\247\303\243o ainda \303\251 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 mas, o menor valor da fun\303\247\303\243o \303\251 agora 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 de forma que, o m\303\241ximo global ocorre para o ponto cr\303\255tico 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 e o de m\303\255nimo global ocorre para o outro ponto cr\303\255tico 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 . Estes resultados s\303\243o confirmados pela Figura 16.7.

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Figura 16.7

Exemplo 16.6: Gr\303\241fico de 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 on LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiYtRiM2Ji1JI21uR0YkNiRRKyZ1bWludXMwOzFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGOC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GNTYkUSIzRidGOEY4RjgvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGK0Y4

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 16.7: <Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GTy9GUlEsMC4xNjY2NjY3ZW1GJy9GVUZobi1GIzYkLUYsNiVRInhGJ0Y2RjlGQC1GPTYtUSIpRidGQEZlbkZFRmZuRklGS0ZNRk9GZ24vRlVRLDAuMTExMTExMWVtRidGQEYrRkAtRj02LVEiPUYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yNzc3Nzc4ZW1GJy9GVUZoby1GIzYpRistRiM2JkYrLUklbXN1cEdGJDYlRlxvLUkjbW5HRiQ2JFEiM0YnRkAvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRitGQC1GPTYtUSgmbWludXM7RidGQEZCRkVGR0ZJRktGTUZPL0ZSUSwwLjIyMjIyMjJlbUYnL0ZVRlxxLUYjNidGYXAtRj02LVExJkludmlzaWJsZVRpbWVzO0YnRkBGQkZFRkdGSUZLRk1GT0ZRRlQtRiM2JkYrLUZfcDYlRlxvLUZicDYkUSIyRidGQEZlcEYrRkBGK0ZARmhwRlxvRkBGK0ZARitGQA==</Equation> em [ 1, 3 ] </Text-field>

Considere a mesma c\303\272bica dos Exemplos 16.5 e 16.6, a saber, a regra:

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

Ly1JImZHNiI2I0kieEdGJSwoKiQpRiciIiQiIiJGLComRitGLClGJyIiI0YsISIiRidGMA==

por\303\251m, que o dom\303\255nio agora seja o intervalo:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUy1GLDYlUSNJN0YnRjZGOS8lK2V4ZWN1dGFibGVHRkRGQEYrRllGQEYrRllGQA==

L14jIiIiNyRGJCIiJA==

os pontos limites do intervalo:

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

NiQiIiIiIiQ=

qualquer ponto estacion\303\241rio (qualquer solu\303\247\303\243o de 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 fora do intervalo ser\303\241 exclu\303\255da posteriormente):

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSZzdGF0N0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

NiQsJiIiIkYkKiYjIiIjIiIkRiQpRigjRiRGJ0YkRiQsJkYkRiRGJSEiIg==

ou qualquer ponto singular dentro do intervalo:

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

O conjunto completo de todos os locais poss\303\255veis para os extremos globais \303\251 formado destas listas com todos os pontos fora do intervalo removidos.

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

NyUiIiIiIiQsJkYjRiMqJiMiIiNGJEYjKUYkI0YjRihGI0Yj

Tudo o que resta \303\251 avaliar a fun\303\247\303\243o em cada um destes pontos, obtendo:

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

NiU3JCIiIiEiJDckIiIkRiU3JCwmRiRGJComIyIiI0YnRiQpRicjRiRGLEYkRiQsJkYnISIiKiYjIiM7IiIqRiRGLUYkRjA=

ou, na forma com ponto flutuante:

NiU3JCQiIiIiIiEkISIkRiY3JCQiIiRGJkYnNyQkIiViQEYoJCElemdGKA==

O maior valor da fun\303\247\303\243o \303\251 agora LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JS1JI21vR0YkNi1RKiZ1bWludXMwO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZJLUkjbW5HRiQ2JFEiM0YnRjVGNUYrRjU=, relativo a ambos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4= e 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 e o menor valor da fun\303\247\303\243o \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GTy9GUlEsMC4xNjY2NjY3ZW1GJy9GVUZobi1GIzYmRistRiM2Jy1JI21uR0YkNiRRIjFGJ0ZALUY9Ni1RIitGJ0ZARkJGRUZHRklGS0ZNRk8vRlJRLDAuMjIyMjIyMmVtRicvRlVGZm8tSSZtZnJhY0dGJDYoLUYjNiQtRl9vNiRRIjJGJ0ZARkAtRiM2JkYrLUkmbXNxcnRHRiQ2Iy1GX282JFEiM0YnRkBGK0ZALyUubGluZXRoaWNrbmVzc0dGYW8vJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXHEvJSliZXZlbGxlZEdGREYrRkBGK0ZALUY9Ni1RIilGJ0ZARmVuRkVGZm5GSUZLRk1GT0Znbi9GVVEsMC4xMTExMTExZW1GJ0ZARitGQC1GPTYtUSI9RidGQEZCRkVGR0ZJRktGTUZPL0ZSUSwwLjI3Nzc3NzhlbUYnL0ZVRmpxLUYjNigtRj02LVEqJnVtaW51czA7RidGQEZCRkVGR0ZJRktGTUZPRlFGVEZlcC1GPTYtUSgmbWludXM7RidGQEZCRkVGR0ZJRktGTUZPRmVvRmdvLUZpbzYoLUYjNictRl9vNiRRIzE2RidGQC1GPTYtUTEmSW52aXNpYmxlVGltZXM7RidGQEZCRkVGR0ZJRktGTUZPRlFGVEZicEYrRkAtRiM2JC1GX282JFEiOUYnRkBGQEZocEZqcEZdcUZfcUYrRkBGK0ZARitGQA== de forma que o m\303\241ximo global ocorre para os dois pontos limites do intervalo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5LUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GV0Y5e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiM0YnRj5GPkYrRj4= e o m\303\255nimo global ocorre para o ponto cr\303\255tico dentro do intervalo, 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 . Estes resultados est\303\243o confirmados pela Figura 16.8.

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Figura 16.8

Exemplo 16.7: Gr\303\241fico de 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 em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiYtRiM2Ji1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGOC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GNTYkUSIzRidGOEY4RjgvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGK0Y4

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 16.8: <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> em <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21vR0YkNi1RIltGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJXRydWVGJy8lKnNlcGFyYXRvckdRJmZhbHNlRicvJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGSi1GIzYoRistRiM2JS1GMjYtUSomdW1pbnVzMDtGJ0Y1L0Y5Rj1GOy9GP0Y9RkBGQkZERkYvRklRJjAuMGVtRicvRkxGVy1GLDYlUScmIzk2MDtGJy8lJ2l0YWxpY0dGPUY1RjUtRjI2LVEiLEYnRjVGVC9GPEY6RlVGQEZCRkRGRkZWL0ZMUSwwLjMzMzMzMzNlbUYnLUYjNiYtSSNtbkdGJDYkUSIyRidGNS1GMjYtUTEmSW52aXNpYmxlVGltZXM7RidGNUZURjtGVUZARkJGREZGRlZGWEZZRjVGK0Y1LUYyNi1RIl1GJ0Y1RjhGO0Y+RkBGQkZERkZGSC9GTFEsMC4xMTExMTExZW1GJ0Y1RitGNQ==">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</Equation> </Text-field>

Considere a fun\303\247\303\243o trigonom\303\251trica :

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

Ly1JImZHNiI2I0kieEdGJSwmLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlRiYiIiItSSRjb3NHRis2IywkKiYiIiNGLkYnRi5GLkYu

no intervalo:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUy1GLDYlUSNJOEYnRjZGOS8lK2V4ZWN1dGFibGVHRkRGQEYrRllGQEYrRllGQA==

L14jIiIiNyQsJEkjUGlHJSpwcm90ZWN0ZWRHISIiLCQqJiIiI0YkRidGJEYk

Note que esta fun\303\247\303\243o \303\251 peri\303\263dica com per\303\255odo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZNLUYsNiVRJyYjOTYwO0YnLyUnaXRhbGljR0Y+RjVGNUYrRjU= e que o intervalo dado \303\251 um per\303\255odo e meio; lembre-se disto quando criar o gr\303\241fico!

Esta fun\303\247\303\243o \303\251 cont\303\255nua em um intervalo limitado e fechado contendo ambos os extremos globais. As poss\303\255veis locais para os pontos de extremos ocorrer s\303\243o:

os pontos limites do intervalo:

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

NiQsJEkjUGlHJSpwcm90ZWN0ZWRHISIiLCQqJiIiIyIiIkYkRipGKg==

qualquer ponto estacion\303\241rio (qualquer solu\303\247\303\243o para 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 fora do intervalo ser\303\241 exclu\303\255da posteriormente):

A derivada 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 \303\251:

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

Ly1JI2YnRzYiNiNJInhHRiUsJi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJUYmIiIiKiYiIiNGLi1JJHNpbkdGKzYjLCQqJkYwRi5GJ0YuRi5GLiEiIg==

e algumas solu\303\247\303\265es da equa\303\247\303\243o 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 s\303\243o:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSNxMkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

NiYsJComIyIiIiIiI0YmSSNQaUclKnByb3RlY3RlZEdGJkYmLCRGJCEiIi1JJ2FyY3Rhbkc2JEYpSShfc3lzbGliRzYiNiMsJComI0YmIiM6RiYpRjVGJUYmRiYsJkYsRitGKEYm

Note que estas s\303\243o solu\303\247\303\265es dentro do intervalo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21vR0YkNi1RIltGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJXRydWVGJy8lKnNlcGFyYXRvckdRJmZhbHNlRicvJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGSi1GIzYnRistRiM2JS1GMjYtUSomdW1pbnVzMDtGJ0Y1L0Y5Rj1GOy9GP0Y9RkBGQkZERkYvRklRJjAuMGVtRicvRkxGVy1GLDYlUScmIzk2MDtGJy8lJ2l0YWxpY0dGPUY1RjUtRjI2LVEiLEYnRjVGVC9GPEY6RlVGQEZCRkRGRkZWL0ZMUSwwLjMzMzMzMzNlbUYnRllGNS1GMjYtUSJdRidGNUY4RjtGPkZARkJGREZGRkgvRkxRLDAuMTExMTExMWVtRidGNUYrRjU=. Pela periodicidade, os pontos estacion\303\241rios correspondentes em 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 s\303\243o obtidos adicionando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiVRIjJGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjgvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkEvJSlzdHJldGNoeUdGQS8lKnN5bW1ldHJpY0dGQS8lKGxhcmdlb3BHRkEvJS5tb3ZhYmxlbGltaXRzR0ZBLyUnYWNjZW50R0ZBLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUC1GLDYmUScmIzk2MDtGJy8lJ2l0YWxpY0dGQUY1RjhGOEYrRjg= a cada ponto estacion\303\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. Todas as solu\303\247\303\265es relevantes s\303\243o ent\303\243o:

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

NiYsJComIyIiJiIiIyIiIkkjUGlHJSpwcm90ZWN0ZWRHRihGKCwkKiYjIiIkRidGKEYpRihGKCwmLUknYXJjdGFuRzYkRipJKF9zeXNsaWJHNiI2IywkKiYjRigiIzpGKClGOSNGKEYnRihGKEYoKiZGJ0YoRilGKEYoLCZGMCEiIiomRi5GKEYpRihGKA==

O conjunto completo de pontos estacion\303\241rios em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21vR0YkNi1RIltGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJXRydWVGJy8lKnNlcGFyYXRvckdRJmZhbHNlRicvJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGSi1GIzYoRistRiM2JS1GMjYtUSomdW1pbnVzMDtGJ0Y1L0Y5Rj1GOy9GP0Y9RkBGQkZERkYvRklRJjAuMGVtRicvRkxGVy1GLDYlUScmIzk2MDtGJy8lJ2l0YWxpY0dGPUY1RjUtRjI2LVEiLEYnRjVGVC9GPEY6RlVGQEZCRkRGRkZWL0ZMUSwwLjMzMzMzMzNlbUYnLUYjNiYtSSNtbkdGJDYkUSIzRidGNS1GMjYtUTEmSW52aXNpYmxlVGltZXM7RidGNUZURjtGVUZARkJGREZGRlZGWEZZRjVGK0Y1LUYyNi1RIl1GJ0Y1RjhGO0Y+RkBGQkZERkZGSC9GTFEsMC4xMTExMTExZW1GJ0Y1RitGNQ== \303\251:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSZzdGF0OEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

NiosJComIyIiIiIiI0YmSSNQaUclKnByb3RlY3RlZEdGJiEiIiwkRiRGJiwkKiYjIiIkRidGJkYoRiZGJiwkKiYjIiImRidGJkYoRiZGJiwmLUknYXJjdGFuRzYkRilJKF9zeXNsaWJHNiI2IywkKiYjRiYiIzpGJilGPkYlRiZGJkYqRihGJiwmRjVGKiomRi9GJkYoRiZGJiwmRjVGJiomRidGJkYoRiZGJkY1

ou qualquer ponto singular localizado no intervalo (as fun\303\247\303\265es seno e cosseno s\303\243o definidas para todos os n\303\272meros reais):

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

O conjunto completo de locais poss\303\255veis para extremos globais \303\251 formado destas listas com todos os pontos fora do intervalo removidos:

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

NyksJEkjUGlHJSpwcm90ZWN0ZWRHISIiLCQqJiIiIyIiIkYkRipGKiwkKiYjRipGKUYqRiRGKkYmLCRGLEYqLCQqJiMiIiRGKUYqRiRGKkYqLCYtSSdhcmN0YW5HNiRGJUkoX3N5c2xpYkc2IjYjLCQqJiNGKiIjOkYqKUY9Ri1GKkYqRiZGJEYqRjQ=

Tudo que resta \303\251 avaliar a fun\303\247\303\243o em cada ponto cr\303\255tico, obtendo:

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

Nik3JCwkSSNQaUclKnByb3RlY3RlZEchIiIiIiI3JCwkKiYiIiNGKEYlRihGKEYoNyQsJComI0YoRixGKEYlRihGJyEiIzckLCRGL0YoIiIhNyQsJComIyIiJEYsRihGJUYoRihGMTckLCYtSSdhcmN0YW5HNiRGJkkoX3N5c2xpYkc2IjYjLCQqJiNGKCIjOkYoKUZFRjBGKEYoRidGJUYoIyIiKiIiKTckRjxGRw==

ou, na forma com ponto flutuante:

Nik3JCQhJVVKISIkJCIiIiIiITckJCIlJUcnRiZGJzckJCElcjpGJiQhIiNGKTckJCIlcjpGJiRGKUYpNyQkIiU4WkYmRjA3JCQiJSopR0YmJCIlRDZGJjckJCIlRkQhIiVGPA==

O maior valor da fun\303\247\303\243o \303\251 agora LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSI5RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JC1GNTYkUSI4RidGOEY4LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZFLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGOA== , obtido para ambos 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 e 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 e o menor valor da fun\303\247\303\243o \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JS1JI21vR0YkNi1RKiZ1bWludXMwO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZJLUkjbW5HRiQ2JFEiMkYnRjVGNUYrRjU= que \303\251 obtido para 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 e 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 . Portanto , o m\303\241ximo globalocorre para os pontos estacion\303\241rios 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 = 0.2527 e 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 = 2.8889 e o m\303\255nimo global ocorre para os pontos estacion\303\241rios, 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 = -1.5708 e 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 = 4.7124. Estes resultado s\303\243o confirmados pela Figura 16.9:

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Figura 16.9

Exemplo 16.8: Gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtRiM2Ji1GOzYtUSIoRidGPi9GQUY2RkMvRkZGNkZHRklGS0ZNL0ZQUSwwLjE2NjY2NjdlbUYnL0ZTRmZuLUYjNiQtRiw2JVEieEYnRjRGN0Y+LUY7Ni1RIilGJ0Y+RllGQ0ZaRkdGSUZLRk1GZW4vRlNRLDAuMTExMTExMWVtRidGPkYrRj4tRjs2LVEiPUYnRj5GQEZDRkVGR0ZJRktGTS9GUFEsMC4yNzc3Nzc4ZW1GJy9GU0Zmby1GIzYoRistRiM2Jy1GLDYlUSRzaW5GJy9GNUZCRj5GOkZURitGPi1GOzYtUSIrRidGPkZARkNGRUZHRklGS0ZNL0ZQUSwwLjIyMjIyMjJlbUYnL0ZTRmRwLUYjNictRiw2JVEkY29zRidGX3BGPkY6LUYjNiZGVi1GIzYmRistRiM2Ji1JI21uR0YkNiRRIjJGJ0Y+LUY7Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y+RkBGQ0ZFRkdGSUZLRk1GT0ZSRmpuRj5GK0Y+Rl1vRj5GK0Y+RitGPkYrRj4= em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiYtRiM2Ji1GLDYlUS4mdW1pbnVzMDsmcGk7RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y7USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSUmcGk7RicvRjhGRUZBRkFGQS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0YrRkE=

Este gr\303\241fico deve parecer ser peri\303\263dico com per\303\255odo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZNLUYsNiVRJyYjOTYwO0YnLyUnaXRhbGljR0Y+RjVGNUYrRjU=. Este ponto ser\303\241 enfatizado mais tarde na Figura 16.10, um gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+RitGPg== sobre um intervalo maior.

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Figura 16.10

Exemplo 16.8: Gr\303\241fico de 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 em 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

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 16.9: <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> em [ -3, 1 ) </Text-field>

Considere uma nova fun\303\247\303\243o criada do primeiro polin\303\264mio encontrado no Exemplo 16.5. A regra para esta fun\303\247\303\243o \303\251:

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

Ly1JImZHNiI2I0kieEdGJSomLCgqJClGJyIiJCIiIkYtKiZGLEYtKUYnIiIjRi0hIiJGJ0YxRi0pLCZGJ0YtRi1GMUYwRjE=

e o dom\303\255nio \303\251 o intervalo 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, dado aqui no Maple pelo comando:

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

L14jIiIiNyQhIiRGJA==

Note que este intervalo n\303\243o \303\251 fechado. N\303\243o \303\251 poss\303\255vel adicionar o limite direito ao intervalo; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYmUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RIj1GJ0Y3L0Y7USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZULUkjbW5HRiQ2JVEiMUYnRjdGQUZBRitGQQ== n\303\243o est\303\241 no dom\303\255nio da fun\303\247\303\243o. Como o intervalo n\303\243o \303\251 fechado, o Teorema 16.2 n\303\243o se aplica. Mas uma ligeira modifica\303\247\303\243o \303\240 nossa abordagem ainda pode ser usada. Primeiro, como:

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

Ly1JJkxpbWl0RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiUqJiwoKiQpSSJ4R0YoIiIkIiIiRjAqJkYvRjApRi4iIiNGMCEiIkYuRjRGMCksJkYuRjBGMEY0RjNGNC9GLkYwSSVsZWZ0R0YoLCRJKWluZmluaXR5R0YmRjQ=

\303\211 claro que n\303\243o existir\303\241 m\303\255nimo global (finito) (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 ). O m\303\241ximo global deve existir (ou seja, ser finito) e ocorrer\303\241 em um ponto cr\303\255tico. Pontos cr\303\255ticos incluem:

os limites do intervalo (note que -1 n\303\243o est\303\241 inclu\303\255do aqui):

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSVlbmQ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjhRJ25vcm1hbEYnRitGOkY9

ISIk

qualquer ponto estacion\303\241rio da fun\303\247\303\243o: A derivada NiMtJSRmfidHNiMlInhH \303\251:

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

Ly1JI2YnRzYiNiNJInhHRiUqJiwqKiQpRiciIiQiIiJGLSomRixGLSlGJyIiI0YtISIiKiYiIihGLUYnRi1GLUYtRi1GLSksJkYnRi1GLUYxRixGMQ==

e as solu\303\247\303\265es da equa\303\247\303\243o 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 s\303\243o:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSZzdGF0OUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

NiUsKComIyIiIiIiJEYmKSwmIiMiKUYmKiZGJ0YmKSIkQCojRiYiIiNGJkYmRiVGJiEiIiomIiIlRiZGKEYwRiZGJkYmLCoqJiNGJiIiJ0YmRihGJkYmKiZGL0YmRihGMEYwRiZGJiooKiZGLkYmXiNGJkYmRiYpRidGLkYmLCZGJEYwRjFGMEYmRiYsKkY0RiZGN0YwRiZGJiooLCRGOUYmRiZGO0YmRjxGJkYw

ou quaisquer pontos singulares situados dentro do intervalo (como mencionado anteriormente, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4= n\303\243o est\303\241 dentro do intervalo semi-aberto, portanto n\303\243o \303\251 considerado aqui):

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

O conjunto completo de poss\303\255veis locais para extremos globais \303\251 formado desta lista com todos os pontos fora do intervalo removidos:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtRiw2JVEmY3JpdDlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSM6PUYnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZTLUYjNictRiw2JVEnc2VsZWN0RidGNkY5LUY9Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRkBGQkZFRkdGSUZLRk1GTy9GUlEmMC4wZW1GJy9GVUZpbi1JKG1mZW5jZWRHRiQ2JC1GIzYpLUYsNiVRK0luSW50ZXJ2YWxGJ0Y2RjktRj02LVEiLEYnRkBGQi9GRkY4RkdGSUZLRk1GT0Zobi9GVVEsMC4zMzMzMzMzZW1GJy1GXG82Ji1GIzYpLUYsNiVRJWVuZDlGJ0Y2RjlGY28tRiw2JVEmc3RhdDlGJ0Y2RjlGY28tRiw2JVEmc2luZzlGJ0Y2RjkvJStleGVjdXRhYmxlR0ZERkBGQC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Zjby1GLDYlUSNJOUYnRjZGOUZmcEZARkBGZnBGQEYrRmZwRkBGK0ZmcEZALUY9Ni1RIjpGJ0ZARkJGRUZHRklGS0ZNRk9GUUZURmZwRkA=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSZjcml0OUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

NyQhIiQsKComIyIiIiIiJEYnKSwmIiMiKUYnKiZGKEYnKSIkQCojRiciIiNGJ0YnRiZGJyEiIiomIiIlRidGKUYxRidGJ0Yn

Tudo que resta \303\251 avaliar a fun\303\247\303\243o em cada destes pontos, obtendo:

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

NiQ3JCEiJCMhI14iIzs3JCwoKiYjIiIiIiIkRiwpLCYiIyIpRiwqJkYtRiwpIiRAKiNGLCIiI0YsRixGK0YsISIiKiYiIiVGLEYuRjZGLEYsRiwsJCoqIiIqRiwsLCIkSChGNiomIiNGRixGMkYsRjYqJiIkOyNGLEYuRixGLCooIiIpRixGLkYsRjJGLEYsKiYiI0tGLClGLyNGNUYtRixGNkYsRi5GNiksJiokRkZGLEYsIiM3RjZGNUY2Riw=

ou, na forma com ponto flutuante:

NiQ3JCQhIiQiIiEkISUpPSRGJTckJCEkTSJGJSQiJWhmISIm

O m\303\241ximo global ocorre para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= = -0.134 com um valor m\303\241ximo um pouco maior que 0. Estes resultados s\303\243o confirmados pela Figura 16.11:

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Figura 16.11

Exemplo 16.9: Gr\303\241fico de 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 em 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

Note que enquanto o gr\303\241fico faz parecer que a fun\303\247\303\243o tem um m\303\241ximo na origem e que possa ser negativa (ou n\303\243o positiva) para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= < 1, vemos que esta afirma\303\247\303\243o \303\251 bem aproximada mas n\303\243o completamente precisa. Uma janela de gr\303\241fico mais apurada na Figura 16.12 mostra o verdadeiro comportamento da fun\303\247\303\243o pr\303\263ximo da origem:

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Figura 16.12

Exemplo 16.9: Gr\303\241fico da 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 localizada para mostrar seus valores positivos

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 16.10: <Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GTy9GUlEsMC4xNjY2NjY3ZW1GJy9GVUZobi1GIzYkLUYsNiVRInhGJ0Y2RjlGQC1GPTYtUSIpRidGQEZlbkZFRmZuRklGS0ZNRk9GZ24vRlVRLDAuMTExMTExMWVtRidGQEYrRkAtRj02LVEiPUYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yNzc3Nzc4ZW1GJy9GVUZoby1JJm1zcXJ0R0YkNiMtRiM2Ji1GPTYtUSkmdmVyYmFyO0YnRkBGQkZFRmZuRklGS0ZNRk9GUUZULUYjNilGKy1GIzYmRistSSVtc3VwR0YkNiVGXG8tSSNtbkdGJDYkUSIyRidGQC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGK0ZALUY9Ni1RKCZtaW51cztGJ0ZARkJGRUZHRklGS0ZNRk8vRlJRLDAuMjIyMjIyMmVtRicvRlVGZHEtRiM2Ji1GanA2JFEiNEYnRkAtRj02LVExJkludmlzaWJsZVRpbWVzO0YnRkBGQkZFRkdGSUZLRk1GT0ZRRlRGXG9GQC1GPTYtUSIrRidGQEZCRkVGR0ZJRktGTUZPRmNxRmVxLUZqcDYkUSIzRidGQEZARl9wRkBGK0ZARitGQA==</Equation> em [ -2, 4 ]</Text-field>

Para nosso exemplo final, encontre os pontos de extremo global (e onde eles ocorrem) para:

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

Ly1JImZHNiI2I0kieEdGJSokKS1JJGFic0clKnByb3RlY3RlZEc2IywoKiQpRiciIiMiIiJGMiomIiIlRjJGJ0YyISIiIiIkRjIjRjJGMUYy

no intervalo:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUy1GLDYlUSRJMTBGJ0Y2RjkvJStleGVjdXRhYmxlR0ZERkBGK0ZZRkBGK0ZZRkA=

L14jIiIiNyQhIiMiIiU=

Porque a fun\303\247\303\243o valor absoluto retorna valores n\303\243o negativos, esta fun\303\247\303\243o \303\251 definida em toda reta real. Em particular, como a fun\303\247\303\243o \303\251 cont\303\255nua no intervalo limitado e fechado LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiYtRiM2Ji1JI21uR0YkNiRRKyZ1bWludXMwOzJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGOC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GNTYkUSI0RidGOEY4RjgvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGO0Y4ela vai conter seus extremos globais em algum lugar neste intervalo.

De forma usual, a procura come\303\247a por localizar todos os pontos cr\303\255ticos no intervalo. Estes incluem:

os limites do intervalo:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSZlbmQxMEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

NiQhIiMiIiU=

quaisquer pontos estacion\303\241rios da fun\303\247\303\243o. A derivada 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 \303\251:

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

Ly1JI2YnRzYiNiNJInhHRiUtSSpwaWVjZXdpc2VHJSpwcm90ZWN0ZWRHNiwyRiciIiIqJiwmIiIjISIiRidGLUYtKSwoKiQpRidGMEYtRi0qJiIiJUYtRidGLUYxIiIkRi0jRi1GMEYxL0YnRi1JKnVuZGVmaW5lZEdGKjJGJ0Y4LCQqJkYvRi0pLChGOEYxRjRGMUY2Ri1GOUYxRjEvRidGOEY7MkY4RidGLg==

e a solu\303\247\303\243o da equa\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEkZn4nRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlMtRiM2Ji1GPTYtUSIoRidGQC9GQ0Y4RkUvRkhGOEZJRktGTUZPL0ZSUSwwLjE2NjY2NjdlbUYnL0ZVRmhuLUYjNiQtRiw2JVEieEYnRjZGOUZALUY9Ni1RIilGJ0ZARmVuRkVGZm5GSUZLRk1GT0Znbi9GVVEsMC4xMTExMTExZW1GJ0ZARitGQC1GPTYtUSI9RidGQEZCRkVGR0ZJRktGTUZPL0ZSUSwwLjI3Nzc3NzhlbUYnL0ZVRmhvLUkjbW5HRiQ2JFEiMEYnRkBGQEYrRkA= \303\251:

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

IiIj

ou quaisquer pontos singulares (da exibi\303\247\303\243o acima, est\303\241 claro que a derivada n\303\243o existe para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiM0YnRj5GPkYrRj4= --- estes valores de x s\303\243o as ra\303\255zes de 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 ):

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtRiw2JVEnc2luZzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUy1GIzYnLUkjbW5HRiQ2JFEiMUYnRkAtRj02LVEiLEYnRkBGQi9GRkY4RkdGSUZLRk1GTy9GUlEmMC4wZW1GJy9GVVEsMC4zMzMzMzMzZW1GJy1GWTYkUSIzRidGQC8lK2V4ZWN1dGFibGVHRkRGQEYrRmFvRkBGK0Zhb0ZALUY9Ni1RIjpGJ0ZARkJGRUZHRklGS0ZNRk9GUUZURmFvRkA=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSdzaW5nMTBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GOFEnbm9ybWFsRidGK0Y6Rj0=

NiQiIiIiIiQ=

O conjunto completo de poss\303\255veis locais para extremos globais \303\251 formado desta lista com todos os pontos fora do intervalo removidos:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSdjcml0MTBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GOFEnbm9ybWFsRidGK0Y6Rj0=

NychIiMiIiUiIiMiIiIiIiQ=

Tudo que resta \303\251 avaliar a fun\303\247\303\243o em cada destes pontos, obtendo:

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

Nic3JCEiIyokKSIjOiMiIiIiIiNGKTckIiIlKiQpIiIkRihGKTckRipGKTckRikiIiE3JEYvRjI=

ou, na forma com ponto flutuante:

Nic3JCQhIiMiIiEkIiV0USEiJDckJCIiJUYmJCIlSzxGKTckJCIiI0YmJCIiIkYmNyRGMiRGJkYmNyQkIiIkRiZGNQ==

O m\303\241ximo global LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJNRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkmbXNxcnRHRiQ2Iy1JI21uR0YkNiRRIzE1RidGPkYrRj5GK0Y+ ocorre para 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 e o m\303\255nimo global LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJtRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4= ocorre para cada ponto singular LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiM0YnRj5GPkYrRj4=. Estes resultados s\303\243o confirmados pela Figura 16.13.

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Figura 16.13

Exemplo 16.10: Gr\303\241fico de 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 em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiYtRiM2Ji1JI21uR0YkNiRRKyZ1bWludXMwOzJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGOC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GNTYkUSI0RidGOEY4RjgvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGK0Y4

<Text-field style="Heading 1" readonly="true" layout="Heading 1">Maple T.A. Maple-Graded Question</Text-field>

<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>

In the following execution group, add an algorithmic variable.

with(plots): with(RandomTools): with(Student[Calculus1]): randomize(): n1 := Generate(choose([2,3,4])): fn1 := sort(Generate(polynom(integer(range=-5..5),x,degree=n1))); n2 := Generate(integer(range=-5..-1)): n3 := Generate(integer(range=1..10)): interval1 := [n2,n3]; dfn1 := diff(fn1,x); rdfn1 := [fsolve(dfn1=0,x)]; #solve(dfn1=0,x); #plot(fn1,x=n2..n3);

LCgqJEkieEc2IiIiIyEiJkYkIiIiIiIkRig=

NyQhIiUiIig=

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y1max := max(eval(fn1,x=n2),eval(fn1,x=n3)): if (y1max = eval(fn1,x=n2)) then x1max := n2; x1min := n3; y1min := eval(fn1, x=-n3); else x1max := n3; x1min := n2; y1min := eval(fn1, x=-n2); end if; if evalb(rdfn1 <> []) then nrdfn1 := nops(rdfn1): j := 0: for i from 1 to nrdfn1 do if (verify(rdfn1[i],n2..n3,interval(closed))=true) then j := j+1: tempval := eval(fn1,x=rdfn1[i]); y1max := max(tempval,y1max); y1min := min(tempval,y1min); if (y1max = tempval) then x1max := rdfn1[i]; elif (y1min = tempval) then x1min := rdfn1[i]; end if; end if; end do; end if; ans4 := evalf[4]({[x1min,y1min,min],[x1max,y1max,max]});

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ISRcIw==

IiIi

IiIh

PCQ3JSQiJSs1ISIlJCIlXUkhIiRJJG1heEclKnByb3RlY3RlZEc3JSQiIigiIiEkISRcI0YvSSRtaW5HRis=

NiI=

JSFH

<Text-field style="Heading 1" layout="Heading 1">Quest\303\243o 16.4</Text-field>

In the following text region, enter the full contents of the question.

Considere a fun\303\247\303\243o f(x) = `$fn1`. Encontre os valores dos extremos globais no intervalo `$interval1`. Entre sua resposta como {[x-coord, y-coord,tipo],[x-coord, y-coord, tipo]}. Insira o tipo como max ou min. Voc\303\252 pode inserir sua resposta com precis\303\243o de 4 d\303\255gitos significativos.

JSFH

<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>

Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed.

ans4; JSFH

<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>

Enter Maple code to evaluate a student's response. To add additional Maple functionality, use the Answer input region.

evalb(evalf(`$ANSWER`,4)=evalf(`$RESPONSE`,4));

<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>

Enter your hints in the following table.

Check the value f(x) at the endpoints and at critical points to find the global extrema.

To find critical points, solve f '(x) = 0, and evaluate f(x) at the resulting x-values.

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea0`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Check the value </mtext><mtext>f(x)</mtext><mtext> at the endpoints and at critical points to find the global extrema.</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea0`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>To find critical points, solve </mtext><mtext>f '(x)</mtext><mtext> = 0, and evaluate </mtext><mtext>f(x)</mtext><mtext> at the resulting </mtext><mtext>x</mtext><mtext>-values.</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>

In the following text region, enter feedback to an incorrect response.

with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea0`, `value`); ANSWER := ans4; ; if evalb(evalf(ANSWER,4)=evalf(eval(parse(StudentResponse)),4)) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!&NewLine;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='{' close='}' separators=','><mrow><mfenced open='[' close=']' separators=','><mrow><mn>0.1000</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>3.050</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>max</mi></mrow></mfenced><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mfenced open='[' close=']' separators=','><mrow><mn>7.</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>249.</mn></mrow><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>min</mi></mrow></mfenced></mrow></mfenced></mrow></mstyle></math><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext></mtext><mtext> </mtext><mtext></mtext><mtext>&NewLine;</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='{' close='}' separators=','><mrow><mfenced open='[' close=']' separators=','><mrow><mn>0.1000</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>3.050</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>max</mi></mrow></mfenced><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mfenced open='[' close=']' separators=','><mrow><mn>7.</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>249.</mn></mrow><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>min</mi></mrow></mfenced></mrow></mfenced></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;

<Text-field style="Heading 1" readonly="true" layout="Heading 1">Maple T.A. Maple-Graded Question</Text-field>

<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>

with(RandomTools): randomize(): testmin := proc(x1,y1,x2,y2) if (y1 < y2) then return (x1,y1); elif (y1 > y2) then return (x2,y2); else return (x1,y1,x2,y2); end if; end: testmax := proc(x1,y1,x2,y2) if (y1 > y2) then return (x1,y1); elif (y2 > y1) then return (x2,y2); else return (x1,y1,x2,y2); end if; end:

a1 := Generate(integer(range=-10..10)): while (a1 = 0) do a1 := Generate(integer(range=-10..10)) end do: b1 := Generate(integer(range=-10..10)): while (b1 = 0) do b1 := Generate(integer(range=-10..10)) end do: c1 := Generate(integer(range=-10..10)): while (evalf(b1^1-4*a1*c1) < 0) do c1 := Generate(integer(range=-10..10)) end do: fn8 := a1*x^2+b1*x+c1; fn9 := sqrt(abs(fn8)); rfn8 := solve(fn8=0,x); dfn9 := simplify(convert(diff(fn9,x),piecewise)): rdfn9 := solve(dfn9=0,x); n17 := Generate(integer(range=-5..-1)): n18 := Generate(integer(range=1..10)): interval3 := [n17,n18];

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cc := 2: x9[1] := evalf(n17): y9[1] := eval(fn9,x=x9[1]): x9[2] := evalf(n18): y9[2] := eval(fn9,x=x9[2]): for bb from 1 to 2 do if (verify(evalf(rfn8[bb]),n17..n18,interval('closed'))=true) then cc := cc+1; x9[cc] := evalf(rfn8[bb]); y9[cc] := eval(fn9,x=x9[cc]); end if; end do; if (verify(evalf(rdfn9),n18..n18,interval('closed'))=true) then cc := cc+1; x9[cc] := evalf(rdfn9); y9[cc] := eval(fn9,x=x9[cc]); end if; convert(x9,list); convert(y9,list); xymin := testmin(x9[1],y9[1],x9[2],y9[2]): xymax := testmax(x9[2],y9[2],x9[2],y9[2]): if (evalf(cc > 2)) then for dd from 3 to cc do xymintemp := testmin(x9[dd],y9[dd],xymin[1],xymin[2]); xymaxtemp := testmax(x9[dd],y9[dd],xymax[1],xymax[2]); if (nops(convert([xymintemp],list)) = 4) and (nops(convert([xymin],list)) > 2 ) then xymin := xymin,x9[dd],y9[dd]; else xymin := xymintemp; end if; if (nops(convert([xymaxtemp],list)) = 4) and (nops(convert([xymax],list)) > 2 ) then xymax := xymax,x9[dd],y9[dd]; else xymax := xymaxtemp; end if; end do: end if: xymin;xymax;

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for ff from 1 to nops(convert([xymin],list))/2 do ans5min[ff] := evalf([xymin[2*ff-1],xymin[2*ff],'min'],4): end do: for gg from 1 to nops(convert([xymax],list))/2 do ans5max[gg] := evalf([xymax[2*gg-1],xymax[2*gg],'max'],4); end do: ans5min2 := op(convert(ans5min,list)): ans5max2 := op(convert(ans5max,list)): ans5 := {ans5min2,ans5max2};

PCQ3JSQhJUB0ISIlJCIlWXghIilJJG1pbkclKnByb3RlY3RlZEc3JSQiIzUiIiEkIiVtPCEiI0kkbWF4R0Yr

JSFH

<Text-field style="Heading 1" layout="Heading 1">Quest\303\243o 16.5</Text-field>

Considere a fun\303\247\303\243o f(x) = `$fn9`. Encontre os extremos globais no intervalo `$interval3`. Insira sua resposta como {[x-coord, y-coord, tipo], etc.}. Insira o tipo como max ou min. Voc\303\252 pode inserir sua resposta com precis\303\243o de 4 d\303\255gitos significativos.

JSFH

<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>

JSFHans5;

JSFH

<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>

evalb(evalf(`$ANSWER`,4)=evalf(`$RESPONSE`,4));

<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>

Check the value f(x) at the endpoints, and singular points and at critical points to find the global extrema.

Find singular points by finding where the derivative is undefined.

To find critical points, solve f '(x) = 0, and evaluate f(x) at the resulting x-values.

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea4`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Check the value </mtext><mtext>f(x)</mtext><mtext> at the endpoints, and singular points and at critical points to find the global extrema.</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea4`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Find singular points by finding where the derivative is undefined. </mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea4`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>To find critical points, solve </mtext><mtext>f '(x)</mtext><mtext> = 0, and evaluate </mtext><mtext>f(x)</mtext><mtext> at the resulting </mtext><mtext>x</mtext><mtext>-values.</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>

Replace this text with feedback.

with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea4`, `value`); ANSWER := ans5; if evalb(evalf(ANSWER,4)=evalf(eval(parse(StudentResponse)),4)) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!&NewLine;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='{' close='}' separators=','><mrow><mfenced open='[' close=']' separators=','><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>0.7321</mn></mrow><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>0.00007746</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>min</mi></mrow></mfenced><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mfenced open='[' close=']' separators=','><mrow><mn>10.</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>17.66</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>max</mi></mrow></mfenced></mrow></mfenced></mrow></mstyle></math><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>&NewLine;</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='{' close='}' separators=','><mrow><mfenced open='[' close=']' separators=','><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>0.7321</mn></mrow><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>0.00007746</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>min</mi></mrow></mfenced><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mfenced open='[' close=']' separators=','><mrow><mn>10.</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>17.66</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi mathvariant='normal'>max</mi></mrow></mfenced></mrow></mfenced></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Resumo</Text-field>

Os dois principais resultados desenvolvidos neste cap\303\255tulo s\303\243o os Teoremas 16.1 e 16.2, repetidos aqui para conveni\303\252ncia do leitor:

Teorema 16.1: Extremos Globais

Em um intervalo limitado e fechado LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiYtRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y7USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJiRidGN0Y6RkFGQS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0YrRkE=, a fun\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= possui seus pontos de m\303\241ximo e de m\303\255nimo global.

Teorema 16.2: Locais de Extremo Global

Seja f uma fun\303\247ao definida em um intervalo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.

Se um valor extremo de f em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 alcan\303\247ado no ponto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= contido no intervalo, ent\303\243o o ponto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= deve ser um ponto cr\303\255tico de f em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= .

Exemplos 16.1 - 16.10 ilustram a aplica\303\247\303\243o destes teoremas e o que pode acontecer quando as hip\303\263teses n\303\243o s\303\243o satisfeitas.

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Pr\303\263ximo Cap\303\255tulo</Text-field>

O pr\303\263ximo degrau no desenvolvimento de uma cole\303\247\303\243o completa de ferramentas para analisar fun\303\247\303\265es \303\251 a an\303\241lise local, tema no pr\303\263ximo cap\303\255tulo. Os cap\303\255tulos de otimiza\303\247\303\243o e gr\303\241ficos completam a discuss\303\243o do uso de c\303\241lculo para localizar e classificar os pontos mais interessantes sobre o gr\303\241fico de uma fun\303\247\303\243o.

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