Question

determine whether Rolle’s Theorem can be applied to f on the closed interval [a,b]. If Rolle’s Theorem can be applied, find all values of in the open interval (a,b) such that f'(c) = ). If Rolle’s Theorem cannot be applied, explain why not.

Answer 1

Given the function f(x) defined by:

`f(x)=3-|x-3|,\text{ for }x\in\lbrack0,6]`

This function is continuous in [0, 6] and is differentiable everywhere except at the point x=3. This point is in the interval [0, 6], and since Rolle's Theorem requires that the function must be differentiable on the open interval (0, 6), we conclude that we can not use the Rolle's Theorem.