Need help on this SAT question

Question

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

f(7)-f(-4) / 7-(-4)

By the Mean Value Theorem, we know there exists a c  in the open interval such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. find it________

Answer 1

(f(7)-f(-4))/(7 - (-4)) = (6 - 7 * (7^2) - (6 - 7 * (-4)^2))/(7 - (-4)) = -7 * (49-16)/11 = -7 * 33/11 = -21

You don't have to calculate the derivative to find c. Just note that the slope changes linearly, so its average is in the middle: (7 + (-4))/2 = 3/2

Since this was labelled an SAT question, I thought that this was the way to solve it.

(The derivative, -14x, does indeed equal -21 at 3/2).