Provide an Appropriate Response $f ( x ) = \left\{ \begin{array} { l l } 7 x & 0 \leq x < 1 \\ 0 & x = 1 \end{array} \right.$

question 118

Essay

Provide an appropriate response.
-The function $f ( x ) = \left\{ \begin{array} { l l } 7 x & 0 \leq x < 1 \\ 0 & x = 1 \end{array} \right.$ is zero at $x = 0$ and $x = 1$ and differentiable on $( 0,1 )$ , but its derivative on $( 0,1 )$ is never zero. Does this example contradict Rolle's Theorem?

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