Answer
The theorem cannot be applied because
$f$ is not continuous on the closed interval $[-1,1]$
($f$ is not defined for $x < 0$)
Work Step by Step
The Mean Value Theorem
If $f$ is continuous on the closed interval $[a, b]$ and differentiable on the open interval $(a, b)$ ,
then there exists a number $c$ in $(a, b)$ such that
$f^{\prime}(c)=\displaystyle \frac{f(b)-f(a)}{b-a}.$
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$f$ is not defined for $x < 0.$
So, $f$ is not continuous on the closed interval $[-1,1]$
The premises of the theorem are not satisfied, so it can not be applied.
