Provide an appropriate response.
-$\text { The function } f ( x ) = \left\{ \begin{array} { l l }
2 x & 0 \leq x

Question

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?

Quizplus · Accepted Answer

The Answer of 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?

Provide an Appropriate Response Is Never Zero