Consider the following function. f(x) = 16-x^(2/3) Find f(-64) and f(64). f(-64) = 0 f(64) = 0 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.) c = -64,64 Based off of this information, what conclusions can be made about Rolle's Theorem?
a. 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).
b. This does not contradict Rolle's Theorem, since f '(0) = 0, and 0 is in the interval (-64, 64).
c. This contradicts Rolle's Theorem, since f(-64) = f(64), there should exist a number c in (-64, 64) such that f '(c) = 0.
d. This does not contradict Rolle's Theorem, since f '(0) does not exist, and so f is not differentiable on (-64, 64).
e. Nothing can be concluded.