Consider the function $f(x) = 2 x^3 - 12 x^2 - 30 x + 2$ on the interval $[ -4 , 10 ]$. 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 $( -4 , 10 )$ such that $f'( c)$ is equal to this mean slope. Find all values of $c$ that work and list them (separated by commas) in the box below. If there are no values of $c$ that work, enter None.

List of numbers: