23. The function f(x) =x has an absolute minimum value at x 0 even though f is not differentiable at x = 0. Is this consistent with the first derivative theorem for local extreme values? Give reasons for your answer. Choose the correct answer below. A. Yes, this is consistent with the first derivative theorem for local extreme values because a function f can possibly have an extreme value at interior points where f' is undefined. B. Yes, this is consistent with the first derivative theorem for local extreme values because there is no smaller value of f nearby. C. No, this is not consistent with the first derivative theorem for local extreme values because x 0 is not in the domain of f D. No, this is not consistent with the first derivative theorem for local extreme values because f' is undefined at x 0

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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23.
The function f(x) =x has an absolute minimum value at x
0 even though f is not differentiable at x = 0. Is this consistent with the first derivative theorem for local extreme values? Give reasons for your answer.
Choose the correct answer below.
A. Yes, this is consistent with the first derivative theorem for local extreme values because a function f can possibly have an extreme value at interior points where f' is undefined.
B. Yes, this is consistent with the first derivative theorem for local extreme values because there is no smaller value of f nearby.
C. No, this is not consistent with the first derivative theorem for local extreme values because x 0 is not in the domain of f
D. No, this is not consistent with the first derivative theorem for local extreme values because f' is undefined at x 0
Transcribed Image Text:23. The function f(x) =x has an absolute minimum value at x 0 even though f is not differentiable at x = 0. Is this consistent with the first derivative theorem for local extreme values? Give reasons for your answer. Choose the correct answer below. A. Yes, this is consistent with the first derivative theorem for local extreme values because a function f can possibly have an extreme value at interior points where f' is undefined. B. Yes, this is consistent with the first derivative theorem for local extreme values because there is no smaller value of f nearby. C. No, this is not consistent with the first derivative theorem for local extreme values because x 0 is not in the domain of f D. No, this is not consistent with the first derivative theorem for local extreme values because f' is undefined at x 0
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