Consider the function f(x)=3−3x2 on the interval

Question

Consider the function  on the interval . Find the average or mean slope of the function on this interval, i.e.

f(8)−f(−6)/8−(−6)=   

By the Mean Value Theorem, we know there exists a  in the open interval  such that  is equal to this mean slope. For this problem, there is only one  that works. Find it.=

Answer 1

(-8+6)/2 = -1

There is a linear change in the slope, so the average slope occurs at the average of the endpoints.