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

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Guia de Estudo de C\303\241lculo

\302\251 Maplesoft, a division of Waterloo Maple Inc., 2005

Cap\303\255tulo 16: An\303\241lise Global

A an\303\241lise de 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 (extrema)global : o mais alto e o mais baixo ponto do gr\303\241fico (graph) de uma fun\303\247\303\243o (function) em um dado dom\303\255nio (domain). Por exemplo, o lugar mais alto e o mais baixo, n\303\243o cobertos pela \303\241gua, na Terra s\303\243o o Mt. Everest (eleva\303\247\303\243o: 8849.8 m) e as margens do Mar Morto (eleva\303\247\303\243o: -411 m). Tranformando 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 (solve) uma grande variedade de problemas aplicados de otimiza\303\247\303\243o (Chapter 19). Eles tamb\303\251m fornecem uma abordagem simples (direta) para fazer o gr\303\241fico de uma fun\303\247\303\243o (function) identificando todos pontos importantes da curva (curve).

Uma aplica\303\247\303\243o imediata de extremo global \303\251 identificar uma vista de janela 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">Cap\303\255tulo Gloss\303\241rio</Text-field>

Os seguintes termos, neste cap\303\255tulo, t\303\252m conex\303\243o com o Dicion\303\241rio de Matem\303\241tica Maple ( Maple Math Dictionary).

absolutevalue

upperbound

interval

continuous

cosine

criticalpoint

curve

cusp

derivative

discontinuity

domain

endpoint

evaluate

extremum

function

minimum

graph

interval

hypothesis

infinite

interval

maximum

minimum

negative

interval

optimization

origin

period

periodicfunction

polynomial

quadratic

realline

real

satisfy

set

sine

singularpoint

solution

solve

trigonometricfunction

unbounded

value

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

restart; with( plots ): with( DocumentTools ):

<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 chave Enter.

InInterval := proc(x,S::list(numeric)) if has(x,I) then return false end if; return evalb( evalf(x)>=op(1,S) and evalf(x)<=op(2,S) ) end proc:

<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). 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 global 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">Notes</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 alcan\303\247ar (conter) os seus pontos de extremo global.)

Se permitirmos para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJNRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRKCYjODczNDtGJ0Y0RjdGPkYrRj4= e 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 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 Pontos de Extremo Global 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 os valores de extremos serem valores da fun\303\247\303\243o. De fato, se definimos como sendo o valor m\303\241ximo (maximum) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJNRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRKCYjODczNDtGJ0Y0RjdGPkYrRj4= para uma fun\303\247\303\243o que n\303\243o tenha um um valor limite superior ( bounded above) e o valor m\303\255nimo como sendo 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 para uma fun\303\247\303\243o que n\303\243o tenha um valor limite inferior (bounded below), 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 Pontos de Extremo global

Em um intervalo limitado e fechado LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiYtRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y7USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJiRidGN0Y6RkFGQS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0YrRkE=, a fun\303\247\303\243o cont\303\255nua LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= cont\303\251m (alcan\303\247a)seus pontos de m\303\241ximo e m\303\255nimo global.

Um bom modo de compreender este teorema \303\251 olhar todas as maneiras em que a hip\303\263tese (hypotheses) 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 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 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 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="Dictionary:Definition,discontinuity" hyperlink="true"> Fechado </Hyperlink></Text-field>

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

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

em um intervalo limitado e fechado 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. Entra-se com ela no Maple como

f1 := piecewise( x< 1, x, x<=2, (x-1)/2 );

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

plot( f1, x=0..2, discont=true, scaling=constrained);

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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 (discontinuous) 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= . Porque 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= . Porque 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 , esta fun\303\247\303\243o cont\303\251m seu ponto de m\303\255nimo global em 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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\243oJSFH.

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 16.2: <Hyperlink linktarget="Dictionary:Definition,continuous" hyperlink="true">Fun\303\247\303\265es Cont\303\255nuas em Intervalos Abertos</Hyperlink></Text-field>

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

f2 := cos(x): f(x) = f2;

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

plot(f2, x=0..2*Pi, tickmarks=[4,[-1,1]]);

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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\241xima global no intervalo aberto 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

Sabemos que a fun\303\247\303\243o cosseno (cosine) \303\251 cont\303\255nua em todo intervalo dos n\303\272meros reais (real numbers). 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 em 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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 (endpoint) do intervalo estivesse incluido (no intervalo), ent\303\243o a fun\303\247\303\243o neste exemplo conteria ambos os pontos de extremo global.

<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

f3 := (1-x^2)/(1+x^2): f(x) = f3;

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

plot(f3, x=-10..10);

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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 (real line) \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\241o h\303\241 nenhum n\303\272mero real para o 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

f4 := 1/x^2: f(x) = f4;

Para qualquer LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJm5lO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1JI21uR0YkNiRRIjBGJ0Y+Rj5GK0Y+. Esta fun\303\247\303\243o \303\251 cont\303\255nua em qualquer intervalo que n\303\243o inclua a origem (origin). Em um intervalo 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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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 = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JkYrLUYjNiZGKy1JJW1zdXBHRiQ2JS1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvRjlRJ2l0YWxpY0YnLUY1NiRRIjJGJ0Y4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRjhGK0Y4LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZVLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGOA== e 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 = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JkYrLUYjNiZGKy1JJW1zdXBHRiQ2JS1GLDYlUSJiRicvJSdpdGFsaWNHUSV0cnVlRicvRjlRJ2l0YWxpY0YnLUY1NiRRIjJGJ0Y4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRjhGK0Y4LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZVLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGOA== . A figura 16.6 mostra o gr\303\241fico desta fun\303\247\303\243o em um intervalo \303\240 direita da origem.

plot(f4, x=0.1 .. 1, y=0..100);

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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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 = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JkYrLUYjNiZGKy1JJW1zdXBHRiQ2JS1GLDYlUSJiRicvJSdpdGFsaWNHUSV0cnVlRicvRjlRJ2l0YWxpY0YnLUY1NiRRIjJGJ0Y4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRjhGK0Y4LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZVLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGOA== e 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 = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JkYrLUYjNiZGKy1JJW1zdXBHRiQ2JS1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvRjlRJ2l0YWxpY0YnLUY1NiRRIjJGJ0Y4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRjhGK0Y4LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZVLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGOA== . a figura 16.5 mostra um gr\303\241fico da fun\303\247\303\243o em um inervalo \303\240 esquerda da origem.

plot(f4, x=-3..-1, y=0..2, view=[-3..0, 0..2]);

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

Figure 16.5

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

em qualquer dos casos, se um ou dos limites do intervalo ou ambos forem omitidos, o intervalo n\303\243o ser\303\241 mais um intervalo fechado e o correspondente ponto de 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 ponto com extremo no infinito nunca pode estar contido!

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

QUESTAO 16.1

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

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Defini\303\247\303\243o: Pontos Estacion\303\241rio, Singular e Cr\303\255tico</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 melhorada ( abetted ??) pela seguinte defini\303\247\303\243o.

Defini\303\247\303\243o 16.2: pontos Estacion\303\241rio, Singular, e Cr\303\255tico

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 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 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, uma esquina ou uma c\303\272spide (cusp).)

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 um ponto cr\303\255tico (critical point) de f em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 um ponto estacion\303\241rio de f em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, 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 Ponto de 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 pontos de extremo global, foi baseada na analise 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 pontos de extremo global, \303\251 como colocar a carro\303\247a na frente dos bois. O conhecimento sobre extremo global \303\251 geralmento usado para selecionar a vista da janela 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: Locais 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) lacaliza\303\247\303\243o(s) para

f5 := x^3 - 3*x^2 - x: f(x) = f5;

no intervalo

I5 := [-2,2]: `I` = I5;

Esta fun\303\247\303\243o \303\251 cont\303\255nua em um intervalo limitado e fechado, de modo que ambos os pontos de extremo global est\303\243o contidos. Acabamos de aprender que as loca\303\247\303\265es poss\303\255veis para pontos de extremo ocorrer 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 lacalizado no intervalo (mas polin\303\264mios (polynomials) n\303\243o tem pontos singulares)

Para este exemplo, n\303\243o existe nenhum ponto singular (nenhum polin\303\264mio tem um ponto singular). Entramos com isto no Maple

sing5 := NULL:

Os pontos estacion\303\241rio s\303\243o as solu\303\247\303\265es (solutions) da equa\303\247\303\243o 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, isto \303\251, de

df5 := diff( f5, x ): q1 := df5 = 0: q1;

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

stat5 := solve( df5=0, x ): stat5;

Os limites do intervalo s\303\243o

end5 := op(I5): end5;

O conjunto completo de loca\303\247\303\265es poss\303\255veis para pontos de extremo global \303\251 formado desta lista com todos os pontos fora do intervalo removidos. A lista de pontos cr\303\255ticos \303\251

crit5 := select( InInterval, [ end5, stat5, sing5 ], I5 );

(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 (evaluate) a fun\303\247\303\243o para cada um destes pontos. Isto leva aos valores

f5a := unapply( f5, x ): q2 := seq( [ X, simplify(f5a(X)) ], X=crit5 );

ou, na vers\303\243o com ponto flutuante,

evalf[4]( q2 );

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 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 , 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.

plot(f5, x=-2..2);

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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

f6 := f5: f(x) = f6;

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

I6 := [-1,3]: `I` = I6;

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

end6 := op(I6): end6;

quaisquer pontos estacion\303\241rios (solu\303\247\303\243o de 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 fora do intervalo ser\303\243o exclu\303\255dos posteriormente)

stat6 := stat5: stat6;

ou quaisquer pontos singulares (mas polin\303\264mios n\303\243o tem pontos singulares).

sing6 := NULL:

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.

crit6 := select( InInterval, [ end6, stat6, sing6 ], I6 );

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

f6a := f5a: q3 := seq( [ X, simplify(f6a(X)) ], X=crit6 );

ou, na vers\303\243o com ponto flutuante,

evalf[4]( q3 );

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 ponto cr\303\255tico 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 e o de m\303\255nimo global ocorre para outro ponto cr\303\255tico LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYjNictSSNtbkdGJDYkUSIxRidGPi1GOzYtUSIrRidGPkZARkNGRUZHRklGS0ZNL0ZQUSwwLjIyMjIyMjJlbUYnL0ZTRmhuLUkmbWZyYWNHRiQ2KC1GIzYkLUZXNiRRIjJGJ0Y+Rj4tRiM2JkYrLUkmbXNxcnRHRiQ2Iy1GVzYkUSIzRidGPkYrRj4vJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl9wLyUpYmV2ZWxsZWRHRkJGK0Y+RitGPkYrRj4= . Estes resultados s\303\243o confirmados pela Figura 16.7.

plot(f6, x=-1..3);

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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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">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</Equation> em [ 1, 3 ] </Text-field>

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

f7 := f5: f(x) = f7;

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

I7 := [1,3]: `I` = I7;

os pontos limites do intervalo

end7 := op(I7): end7;

qualquer ponto estacion\303\241rio (solu\303\247\303\243o de 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 fora do intervalo ser\303\241 excluido posteriormente)

stat7 := stat5: stat7;

ou qualquer ponto singular dentro do intervalo(mas polin\303\264mios n\303\243o tem pontos singulares).

sing7 := NULL:

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.

crit7 := select( InInterval, [ end7, stat7, sing7 ], I7 );

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

f7a := f5a: q4 := seq( [ X, simplify(f7a(X)) ], X=crit7 );

ou, na vers\303\243o com ponto flutuante,

evalf[4]( q4 );

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 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 de forma que o m\303\241ximo global ocorre para os dois pontos limites do intervalo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4=e 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.

plot(f7, x=1..3, view=[0..4, -7..0]);

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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="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">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</Equation> </Text-field>

Considere a fun\303\247\303\243o trigonom\303\251trica (trigonometric)

f8 := sin(x)+cos(2*x): f(x) = f8;

no intervalo

I8 := [-Pi,2*Pi]: `I` = I8;

Note que esta fun\303\247\303\243o \303\251 peri\303\263dica (periodic) com per\303\255odo (period) 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 pontos de extremo global. As poss\303\255veis locais para os pontos de extremos ocorrer s\303\243o

os pontos limites do intervalo

end8 := op(I8): end8;

qualquer ponto estacion\303\241rio (qualquer solu\303\247\303\243o para 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 fora do intervalo ser\303\241 excluido posteriormente)

A derivada (derivative) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSRmfidGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUTAmQXBwbHlGdW5jdGlvbjtGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlQtRiM2Ji1GOzYtUSIoRidGQS9GREY2RkYvRklGNkZKRkxGTkZQL0ZTUSwwLjE2NjY2NjdlbUYnL0ZWRmluLUYjNiQtRiw2JVEieEYnRjRGN0ZBLUY7Ni1RIilGJ0ZBRmZuRkZGZ25GSkZMRk5GUEZobi9GVlEsMC4xMTExMTExZW1GJ0ZBRitGQUYrRkE= \303\251

df8 := collect(diff( f8, x ),[sin,cos]): `f'`(x) = df8;

e algumas solu\303\247\303\265es da equa\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEkZn4nRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEwJkFwcGx5RnVuY3Rpb247RicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRy8lKXN0cmV0Y2h5R0ZHLyUqc3ltbWV0cmljR0ZHLyUobGFyZ2VvcEdGRy8lLm1vdmFibGVsaW1pdHNHRkcvJSdhY2NlbnRHRkcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZWLUYjNiYtRj02LVEiKEYnRkMvRkZGOEZIL0ZLRjhGTEZORlBGUi9GVVEsMC4xNjY2NjY3ZW1GJy9GWEZbby1GIzYkLUYsNiVRInhGJ0Y2RjlGQy1GPTYtUSIpRidGQ0ZobkZIRmluRkxGTkZQRlJGam4vRlhRLDAuMTExMTExMWVtRidGQ0YrRkMtRj02LVEiPUYnRkNGRUZIRkpGTEZORlBGUi9GVVEsMC4yNzc3Nzc4ZW1GJy9GWEZbcC1JI21uR0YkNiRRIjBGJ0ZDRkNGK0ZD s\303\243o

q1 := df8 = 0: q2 := solve( q1, x ): q2;

Note que estas s\303\243o solu\303\247\303\265es dentro do intervalo 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. 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

q3 := op(map( x->x+2*Pi, [q2] ));

O conjunto completo de pontos estacion\303\241rios em 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 \303\251

stat8 := op( { q2, q3 } ): stat8;

ou qualquer ponto singular localizado no intervalo (ambos seno (sine) e cosseno s\303\243o definidos para todos os n\303\272meros reais)

sing8 := NULL:

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

crit8 := select( InInterval, [ end8, stat8, sing8 ], evalf(I8) );

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

f8a := unapply( f8, x ): q4 := seq( [ X, simplify(f8a(X)) ], X=crit8 );

ou, na vers\303\243o com ponto flutuante,

evalf[4]( q4 );

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 global ocorre 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.

plot(f8, x=-Pi..2*Pi,tickmarks=[5,3]);

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

Figura 16.9

Exemplo 16.8: Gr\303\241fico de 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 em 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

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 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 sobre um intervalo mais maior.

plot(f8, x=-3*Pi...3*Pi,tickmarks=[6,3]);

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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

f9 := f5/(x-1)^2: f(x) = f9;

e o dom\303\255nio \303\251 o intervalo 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, dado (aqui) no Maple pelo

I9 := [-3,1]: `I` = I9;

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. Por que o intervalo n\303\243o \303\251 fechado, Teorema 16.2 n\303\243o se aplica. Mas, uma ligeira modifica\303\247\303\243o \303\240 nossa abordagem ainda pode ser usadas. Primeiro, por que

q1 := Limit( f9, x=1, left ): q1 = value( q1 );

\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 (i.e., 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)

end9 := -3: end9;

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

df9 := simplify(diff( f9, x )): `f'`(x) = df9;

e as solu\303\247\303\265es da equa\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEkZn4nRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEwJkFwcGx5RnVuY3Rpb247RicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRy8lKXN0cmV0Y2h5R0ZHLyUqc3ltbWV0cmljR0ZHLyUobGFyZ2VvcEdGRy8lLm1vdmFibGVsaW1pdHNHRkcvJSdhY2NlbnRHRkcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZWLUYjNiYtRj02LVEiKEYnRkMvRkZGOEZIL0ZLRjhGTEZORlBGUi9GVVEsMC4xNjY2NjY3ZW1GJy9GWEZbby1GIzYkLUYsNiVRInhGJ0Y2RjlGQy1GPTYtUSIpRidGQ0ZobkZIRmluRkxGTkZQRlJGam4vRlhRLDAuMTExMTExMWVtRidGQ0YrRkMtRj02LVEiPUYnRkNGRUZIRkpGTEZORlBGUi9GVVEsMC4yNzc3Nzc4ZW1GJy9GWEZbcC1JI21uR0YkNiRRIjBGJ0ZDRkNGK0ZD s\303\243o

q1 := df9 = 0: stat9 := solve( q1, x ): stat9;

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

sing9 := NULL: sing9;

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

crit9 := select( InInterval, [ end9, stat9, sing9 ], I9 ): crit9;

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

f9a := unapply( f9, x ): q2 := seq( [ X, simplify(f9a(X)) ], X=crit9 );

ou, na vers\303\243o com ponto flutuante,

evalf[4]( q2 );

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

plot(f9, x=-3..1, y=-50..10);

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

Figura 16.11

Exemplo 16.9: Gr\303\241fico de 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 em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2I1EhRictSSNtb0dGJDYtUSJbRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSV0cnVlRicvJSpzZXBhcmF0b3JHUSZmYWxzZUYnLyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRLDAuMTY2NjY2N2VtRicvJSdyc3BhY2VHRkgtSSNtbkdGJDYkUSsmdW1pbnVzMDszRidGMy1GMDYtUSIsRidGMy9GN0Y7L0Y6RjgvRj1GO0Y+RkBGQkZEL0ZHUSYwLjBlbUYnL0ZKUSwwLjMzMzMzMzNlbUYnLUZMNiRRIjFGJ0YzLUYwNi1RIilGJ0YzRjZGOUY8Rj5GQEZCRkRGRi9GSlEsMC4xMTExMTExZW1GJ0Yz

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 pode ser negativa (ou n\303\243o positiva ) para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= < 1, Isto \303\251 aproximado mas n\303\243o completamente preciso. Uma janela do gr\303\241fico mais conservativa na Figura 16.12 mostra o verdadeiro comportamento da fun\303\247\303\243o pr\303\263ximo da origem

plot(f9, x=-3..1, y=-2..1);

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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">Exempl 16.10: <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> em [ -2, 4 ]</Text-field>

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

f10 := sqrt( abs(x^2-4*x+3) ): f(x) = f10;

no intervalo

I10 := [-2,4]: `I` = I10;

Porque a fun\303\247\303\243o m\303\272dulo (absolute value) retorna (d\303\241) 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 seu pontos de extremo global em algum lugar neste intervalo.

Como o usual, a procura come\303\247a por localizar podos os pontos cr\303\255ticos no intervalo. Estes incluem

os limites do intervalo

end10 := op(I10): end10;

NiQhIiMiIiU=

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

df10 := simplify(diff( f10, x )): `f'`(x) = convert(df10,piecewise,x);

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

e a solu\303\247\303\243o da equa\303\247\303\243o 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 \303\251

q1 := df10 = 0: stat10 := solve( q1, x ): stat10;

IiIj

ou quaisquer pontos singulares (do mostrado acima, est\303\241 claro que a derivada n\303\243o existe para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiM0YnRj5GPkYrRj4= --- Estes s\303\243o as raizes de 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 )

sing10 := 1,3: sing10;

NiQiIiIiIiQ=

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

crit10 := select( InInterval, [ end10, stat10, sing10 ], I10 ): crit10;

NychIiMiIiUiIiMiIiIiIiQ=

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

f10a := unapply( f10, x ): q2 := seq( [ X, simplify(f10a(X)) ], X=crit10 );

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjPkkjcTJHRiY2JzckISIjKiQpIiM6IyIiIiIiI0YzNyQiIiUqJCkiIiRGMkYzNyRGNEYzNyRGMyIiITckRjlGPDcnRi1GNUY6RjtGPQ==

ou, na vers\303\243o com ponto flutuante,

evalf[4]( q2 );

Nic3JCQhIiMiIiEkIiV0USEiJDckJCIiJUYmJCIlSzxGKTckJCIiI0YmJCIiIkYmNyRGMiRGJkYmNyQkIiIkRiZGNQ==

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

plot(f10, x=-2..4);

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

Figura 16.13

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

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

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Cap\303\255tulo Sum\303\241rio</Text-field>

Os dois resultados principais 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: Pontos de Extremo Global Incluidos (Attainment)

Em um intervalo limitado e fechado LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiYtRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y7USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJiRidGN0Y6RkFGQS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0YrRkE=, a fun\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= cont\303\251m 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=.

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 (satisfied).

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Qual \303\251 o Pr\303\263ximo?</Text-field>

O pr\303\263ximo degrau no desenvolvimento de uma cole\303\247\303\243o completa de ferramentas para analizar fun\303\247\303\265es \303\251 An\303\241lise Local (Local Analysis) no pr\303\263ximo cap\303\255tulo. Os cap\303\255tulos de Otimiza\303\247\303\243o e Gr\303\241ficos (Graphing) completa 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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