Answer
See explanations.
Work Step by Step
This does not contradict the corollary of the Mean Value Theorem where the Theorem requires the derivative to be zero for all $x$ values in the domain. In the case of $f(x)=x^2$, we have $f’(x)=2x$ which is zero at only one point ($x=0$), while for $x\ne0, f’(x)\ne0$.
