Consider the following function. f(x) = 4x2/3 Find f(-8) and f(8). f(-8) = f(8) = Find all values c in (-8, 8) such that f'(c) = 0. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) C= Based off of this information, what conclusions can be made about Rolle's Theorem? O This contradicts Rolle's Theorem, since f is differentiable, f(-8)= f(8), and f'(c) = 0 exists, but c is not in (-8, 8). O This does not contradict Rolle's Theorem, since f'(0) = 0, and 0 is in the interval (-8, 8). O This contradicts Rolle's Theorem, since f(-8)= f(8), there should exist a number c in (-8, 8) such that f'(c) = 0. O This does not contradict Rolle's Theorem, since f'(0) does not exist, and so f is not differentiable on (-8, 8).
Consider the following function. f(x) = 4x2/3 Find f(-8) and f(8). f(-8) = f(8) = Find all values c in (-8, 8) such that f'(c) = 0. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) C= Based off of this information, what conclusions can be made about Rolle's Theorem? O This contradicts Rolle's Theorem, since f is differentiable, f(-8)= f(8), and f'(c) = 0 exists, but c is not in (-8, 8). O This does not contradict Rolle's Theorem, since f'(0) = 0, and 0 is in the interval (-8, 8). O This contradicts Rolle's Theorem, since f(-8)= f(8), there should exist a number c in (-8, 8) such that f'(c) = 0. O This does not contradict Rolle's Theorem, since f'(0) does not exist, and so f is not differentiable on (-8, 8).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
Related questions
Question
![Consider the following function.
f(x) = 4x2/3
Find f(-8) and f(8).
f(-8) =
f(8) =
Find all values c in (-8, 8) such that f'(c) = 0. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
C =
Based off of this information, what conclusions can be made about Rolle's Theorem?
O This contradicts Rolle's Theorem, since f is differentiable, f(-8) = f(8), and f'(c) = 0 exists, but c is not in (-8, 8).
O This does not contradict Rolle's Theorem, since f'(0) = 0, and 0 is in the interval (-8, 8).
O This contradicts Rolle's Theorem, since f(-8)= f(8), there should exist a number c in (-8, 8) such that f'(c) = 0.
O This does not contradict Rolle's Theorem, since f'(0) does not exist, and so f is not differentiable on (-8, 8).
O Nothing can be concluded.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46d42788-da92-4224-9c90-774b9742bbda%2Fc438c0aa-ec05-4d68-bde9-56a8209599f7%2Fbrs37we_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following function.
f(x) = 4x2/3
Find f(-8) and f(8).
f(-8) =
f(8) =
Find all values c in (-8, 8) such that f'(c) = 0. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
C =
Based off of this information, what conclusions can be made about Rolle's Theorem?
O This contradicts Rolle's Theorem, since f is differentiable, f(-8) = f(8), and f'(c) = 0 exists, but c is not in (-8, 8).
O This does not contradict Rolle's Theorem, since f'(0) = 0, and 0 is in the interval (-8, 8).
O This contradicts Rolle's Theorem, since f(-8)= f(8), there should exist a number c in (-8, 8) such that f'(c) = 0.
O This does not contradict Rolle's Theorem, since f'(0) does not exist, and so f is not differentiable on (-8, 8).
O Nothing can be concluded.
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