Consider the function f$($x$)=2$x$^(3)-9$x$^(2)-108$x$+1$ on the interval $-6,7.$ Find the average or mean

slope of the function on this interval.

By the Mean Value Theorem, we know there exists a c in the open interval $(-6,7)$ such that f$^(\text{'})($c$)$ is

equal to this mean slope. For this problem, there are two values of c that work.

$3\mathrm{.}2$

The smaller one is

and the larger one is