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 $$[0, 2]$$?