Find all values c in (−1, 1) such that f '(c) = 0. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)c =

Consider the following function.f(x) = 1 − x2/3Find f(−1) and f(1).f(−1)= 0 f(1)= 0 Find all values c in (−1, 1) 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(−1) = f(1), and f '(c) = 0 exists, but c is not in (−1, 1).This does not contradict Rolle's Theorem, since f '(0) = 0, and 0 is in the interval (−1, 1).    This contradicts Rolle's Theorem, since f(−1) = f(1), there should exist a number c in (−1, 1) 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 (−1, 1).Nothing can be concluded

Use the given graph to estimate the value of each derivative. (Round all answers to one decimal place.)(a) f ' (-3) (b) f ' (-2) (c) f ' (-1) (d) f ' (0) (e) f ' (1)

The derivative of the function f is give by 𝑓′(𝑥)=3𝑥+4𝑥2. The point (-1,0) lie on the graph of f. Find an expression for f.What is the c value?f(x)= 𝑥2 +𝑥3 -

Based off of this information, what conclusions can be made about Rolle's Theorem?This contradicts Rolle's Theorem, since f is differentiable, f(−1) = f(1), and f '(c) = 0 exists, but c is not in (−1, 1).This does not contradict Rolle's Theorem, since f '(0) = 0, and 0 is in the interval (−1, 1).    This contradicts Rolle's Theorem, since f(−1) = f(1), there should exist a number c in (−1, 1) 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 (−1, 1).Nothing can be concluded.

Verify that the function satisfies the three hypotheses of Rolle's theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's theorem. (Enter your answers as a comma-separated list.)f(x) = 3x2 − 6x + 4,   [−1, 3]