Suppose f(x)= 7-8x^2, by the Mean Value Theorem, we know there exists a c in the open interval (-2,5) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

Question

Suppose f(x)= 7-8x^2, by the Mean Value Theorem, we know there exists a c in the open interval (-2,5) such that f'(c) is equal to this mean slope.  For this problem, there is only one c that works. Find it.

Steve · Answer

f(-2) = -25 f(5) = -193 mean slope is (-193+25)/7 f' = -16x find where f' = the mean slope. That is c. Make sure it is in (-2,5).