We have,

$f\left(x\right)=\left|x\right|$

We know that the function is not differentiable at the sharp edges. Hence, $f\left(x\right)$ is not differentiable at $x=0$.  Therefore, Rolle's theorem is not applicable for the function

$f\left(x\right)=\left|x\right|$ in $[-1,1]$

$\because f^{\text{'}}\left(0\right)$ does not exist.