Let a < b. Let f be a function defined on [a, b]. Assume f satisfies the hypotheses of the Mean Value Theorem. Which of the following statements is true? Select all that apply. IF Vx € (a, b), f'(x) = 0, THEN f is constant on (a,b). IF 3c (a, b) such that f'(c) > 0, THEN f(b) > f(a).

Let a < b. Let f be a function defined on [a, b]. Assume f satisfies the hypotheses of the Mean Value Theorem. Which of the following statements is true? Select all that apply. IF Vx € (a, b), f'(x) = 0, THEN f is constant on (a,b). IF 3c (a, b) such that f'(c) > 0, THEN f(b) > f(a).

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.

Chapter3: The Derivative

Section3.CR: Chapter 3 Review

Problem 12CR: Determine whether each of the following statements is true or false and explain why. The derivative...

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Question

Plz answer correctly asap plz only correct answer plz

Let a < b.
Let f be a function defined on [a, b].
Assume f satisfies the hypotheses of the Mean Value Theorem.
Which of the following statements is true?
Select all that apply.
IF Va € (a, b), f'(x) = 0, THEN f is constant on (a,b).
IF 3c
(a, b) such that f'(c) > 0, THEN f(b) > f(a).
IF 3c
(a, b) such that f'(c) = 0, THEN f(b) = f(a).
3c (a, b) such that f(b) f(a) = f'(c)(b-a)
IF f(b) > f(a), THEN c € (a, b) such that f'(c) > 0.
-

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