Consider the function $f(x) = 7 - 3x^2$ on the interval $[-6, 6]$. Find the average or mean slope of the function on this interval, i.e.
$\frac{f(6) - f(-6)}{6 - (-6)} =$
By the Mean Value Theorem, we know there exists a $c$ in the open interval $(-6, 6)$ such that $f'(c)$ is equal to this mean slope. For this problem, there is only one $c$ that works. Find it.