Consider the function f(x) = 7 - 3x2 on the interval [-2, 4].
A) Find the average or mean slope of the function on this interval, i.e. f(4)- f(-2) 4 - (-2)=?
B) By the Mean Value Theorem, we know there exists a c in the open interval (-2, 4) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.