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8. . [0/1.42 Points] DETAILS PREVIOUS ANSWERS SCALC9 3.2.013. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following function. RX) = 1 - x2/3 Find R(-1) and f( 1 ) . R( - 1 ) = X - 185 f(1) = X 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.) Based off of this information, what conclusions can be made about Rolle's Theorem? This contradicts Rolle's Theorem, since fis 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. 9. [0.71/1.42 Points] DETAILS PREVIOUS ANSWERS SCALC9 3.2.015. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f( x ) = 2x2 - 3x + 1, [0 , 2] Yes, it does not matter if f is continuous or differentiable, every function satisfies the Mean Value Theorem. Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable on RR. No, f is not continuous on [0, 2]. No, f is continuous on [0, 2] but not differentiable on (0, 2). There is not enough information to verify if this function satisfies the Mean Value Theorem. If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE)