Consider the function $f(x) = 3x^3 - 4x$ on the interval $[-4, 4]$. Find the average or mean slope of the function on this interval.
By the Mean Value Theorem, we know there exists at least one $c$ in the open interval $(-4, 4)$ such that $f'(c)$ is equal to this mean slope.
For this problem, there are two values of $c$ that work.
The smaller one is
and the larger one is