Provide an Appropriate Response Is Never Zero

question 240

Essay

Provide an appropriate response.
- $\text { The function } f ( x ) = \left\{ \begin{array} { l l } 2 x & 0 \leq x < 1 \\0 & x = 1\end{array} \text { is zero at } x = 0 \text { and } x = 1 \text { and differentiable on } ( 0,1 ) \text {, but its derivative on ( } 0,1 \right)$ is never zero. Does th is example contradict Rolle's Theorem?

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