Consider the following function. f(x) = 16 - x^(2/3) Find f(-64) and f(64). Find all values c in (-64, 64) such that f'(c) = 0

Question

Consider the following function.
f(x) = 16 - x^(2/3)
Find f(-64) and f(64).
Find all values c in (-64, 64) 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?
This contradicts Rolle's Theorem, since f is differentiable, f(-64) = f(64), and f'(c) = 0 exists, but c is not in (-64, 64).
This does not contradict Rolle's Theorem, since f(0) = 0, and 0 is in the interval (-64, 64).
This contradicts Rolle's Theorem, since f(-64) = f(64), there should exist a number c in (-64, 64) 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 (-64, 64).
Nothing can be concluded.

Kunduz · Accepted Answer

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