Consider the following function. f(x) = 4 – x2/3 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.) 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. 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.

Consider the following function. f(x) = 4 – x2/3 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.) 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. 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.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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