1. Let f(x) = 1 – x2/3. Show that f(1) = f(-1). This means that by Rolle's the- orem there should be a point c in (–1,1) such that f'(c) = 0. However, there is no such point (you can verify by taking the derivative). Why does this example not contradict Rolle's theorem ? %3D

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Let f(x) = 1 – x2/3. Show that f(1) = f(-1). This means that by Rolle's the-
orem there should be a point c in (-1, 1) such that f'(c) = 0. However, there is
no such point (you can verify by taking the derivative). Why does this example
not contradict Rolle's theorem ?
%3D
Transcribed Image Text:1. Let f(x) = 1 – x2/3. Show that f(1) = f(-1). This means that by Rolle's the- orem there should be a point c in (-1, 1) such that f'(c) = 0. However, there is no such point (you can verify by taking the derivative). Why does this example not contradict Rolle's theorem ? %3D
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