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According to Fermat's Theorem: If f has a local maximum or minimum at c, and if f'(c) exists, then f'(c) = 0. However, we must be careful when using Fermat's Theorem. Even when f'(c) = 0 there need not be a maximum or minimum at c. Furthermore, there may be an extreme value even when f'(c) does not exist. Give two examples (one of each) of specific functions f and values of c that demonstrate the following two cases:       1.  f'(c) = 0 but f has no maximum or minimum at c      2.  f has a maximum or minimum at c but f'(c) does not exist

According to Fermat's Theorem: If f has a local maximum or minimum at c, and if f'(c) exists, then f'(c) = 0. However, we must be careful when using Fermat's Theorem. Even when f'(c) = 0 there need not be a maximum or minimum at c. Furthermore, there may be an extreme value even when f'(c) does not exist. Give two examples (one of each) of specific functions f and values of c that demonstrate the following two cases:       1.  f'(c) = 0 but f has no maximum or minimum at c      2.  f has a maximum or minimum at c but f'(c) does not exist

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
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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According to Fermat's Theorem: If f has a local maximum or minimum at c, and if f'(c) exists, then f'(c) = 0. However, we must be careful when using Fermat's Theorem. Even when f'(c) = 0 there need not be a maximum or minimum at c. Furthermore, there may be an extreme value even when f'(c) does not exist.

Give two examples (one of each) of specific functions f and values of c that demonstrate the following two cases: 

     1.  f'(c) = 0 but f has no maximum or minimum at c

     2.  f has a maximum or minimum at c but f'(c) does not exist

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