Consider the function $f(x)=2x^3-9x^2-24x+3on$ the interval $-5,10.$ Find the average $or$ mean

slope $of$ the function $on$ this interval.

$By$ the Mean Value Theorem, $we$ know there exists $acin$ the open interval $(-5,10)$ such that $f^{\text{'}}(c)is$

equal $to$ this mean slope. For this problem, there are two values $ofc$ that work.

The smaller one $is$

and the larger one $is$