Consider the function $f(x) = 3x^2 + 5x + 11$ on the interval $[-3, 6]$. The average or mean slope of the function on this interval is 14.
By the Mean Value Theorem, we know there exists a $c$ in the open interval $(-3, 6)$ such that $f'(c)$ is equal to this mean slope. For this problem, there is only one $c$ that works.