Consider the function f(x)=2−4x2 on the interval [−5,8]. Find the average or mean slope of the function on this interval, i.e.
By the Mean Value Theorem, we know there exists a c in the open interval (−5,8) such that f′(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

Question

Consider the function f(x)=2−4x2 on the interval [−5,8]. Find the average or mean slope of the function on this interval, i.e.
By the Mean Value Theorem, we know there exists a c in the open interval (−5,8) such that f′(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

jim_thompson5910 · Answer

first you need to compute 

$$\Large \frac{f(8)-f(-5)}{8 - (-5)}$$

to get the average rate of change