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Mathematics, 21.04.2020 16:11 yddlex

Consider the following function. f ( x ) = 1 βˆ’ x 2 / 3 Find f ( βˆ’ 1 ) and f ( 1 ) . f ( βˆ’ 1 ) = f ( 1 ) = Find all values c in ( βˆ’ 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 ( βˆ’ 1 ) = f ( 1 ) , there should exist a number c in ( βˆ’ 1 , 1 ) such that f ' ( c ) = 0 . This does not contradict Rolle's Theorem, since f ' ( 0 ) = 0 , and 0 is in the interval ( βˆ’ 1 , 1 ) . This does not contradict Rolle's Theorem, since f ' ( 0 ) does not exist, and so f is not differentiable on ( βˆ’ 1 , 1 ) . This contradicts Rolle's Theorem, since f is differentiable, f ( βˆ’ 1 ) = f ( 1 ) , and f ' ( c ) = 0 exists, but c is not in ( βˆ’ 1 , 1 ) . Nothing can be concluded.

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Consider the following function. f ( x ) = 1 βˆ’ x 2 / 3 Find f ( βˆ’ 1 ) and f ( 1 ) . f ( βˆ’ 1 ) = f (...
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