Mean Value Theorem Application

The function $f$ has a derivative given by $f'(x) = (x + 1)\cos(\pi x)$. If $f(0) = \frac{1}{\pi^2}$ and $f(2) = \frac{1}{\pi^2}$, how many values of $x$ in the open interval $(0, 2)$ satisfy the conclusion of the Mean Value Theorem for $f$ on the closed interval $[0, 2]$?