Mean Value Theorem Application

Let $f$ be the function defined by $f(x) = \displaystyle \frac{1}{4}x^4 - \frac{2}{3}x^3 + \frac{1}{2}x^2 - \frac{1}{2}x$. For how many values of $x$ in the interval $(0, 1.565)$ is the instantaneous rate of change of $f$ equal to its average rate of change on the interval $[0, 1.565]$?