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Provide an Appropriate Response Is Never Zero

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Essay

Provide an appropriate response.
-  The function f(x)={2x0x<10x=1 is zero at x=0 and x=1 and differentiable on (0,1), but its derivative on ( 0,1)\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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