Consider the following function. f(x) = 9 − x2/3 Find f(−27) and f(27). f(−27) = f(27) = Find all values c in (−27, 27) such tha
t 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(−27) = f(27), and f '(c) = 0 exists, but c is not in (−27, 27). This does not contradict Rolle's Theorem, since f '(0) = 0, and 0 is in the interval (−27, 27). This contradicts Rolle's Theorem, since f(−27) = f(27), there should exist a number c in (−27, 27) 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 (−27, 27). Nothing can be concluded.
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