Intervals - calculus

Question

Consider the function ` f(x) = 7 -8 x^2 ` on the interval ` [ -4 , 8 ] `. Find the average or mean slope of the function on this interval, i.e.

` \frac ( f(8) - f(-4) )( 8 - (-4) ) = ` __________________ 

By the Mean Value Theorem, we know there exists a c in the open interval ` (-4, 8) ` 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(8)-f(-4))/(8-(-4)) = (-505 -(-121))/12 = -32

f '(x) = -16x

f' '(c) = -16c = -32 --> c = 2