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Give an example showing that, even if f 0 (c) = 0, it could happen that f(x) does not have a local maximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?

Give an example showing that, even if f 0 (c) = 0, it could happen that f(x) does not have a local maximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 1CR
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2. Give an example showing that, even if f
0
(c) = 0, it could happen that f(x) does not have a local
maximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?

2. Give an example showing that, even if f'(c) = 0, it could happen that f(x) does not have a local maximum or minimum at I = c. How is this consistent with Fermat's Theorem in the book?
Transcribed Image Text:2. Give an example showing that, even if f'(c) = 0, it could happen that f(x) does not have a local maximum or minimum at I = c. How is this consistent with Fermat's Theorem in the book?
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