Consider the following function. f(x) = 4x^2/3 Find f(-8) and f(8). f(-8) f(8) = Find all values c in (-8, 8) such that f'(c) =

Question

Consider the following function.
f(x) = 4x^2/3
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?
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).
This does not contradict Rolle's Theorem, since f'(0) = 0, and 0 is in the interval (-8, 8).
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 condict Rolle's Theorem, since f'(0) does not exist, and so f is not differentiable on (-88).
Nothing can be concluded.

Kunduz · Accepted Answer

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