Consider the following function. f ( x ) = 1 − x 2 / 3 Find f ( − 1 ) and f ( 1 ) . f ( − 1 ) = f ( 1 ) = 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 ( − 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 ) = 0 , and 0 is in the interval ( − 1 , 1 ) . This does not contradict Rolle's Theorem, since f ' ( 0 ) does not exist, and so f is not differentiable on ( − 1 , 1 ) . 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 ) . Nothing can be concluded.