FInd C and the slope

Question

Consider the function f(x) = 4 -8 x^2 on the interval [ -6 , 4 ]. Find the average or mean slope of the function on this interval, i.e.

f(4)- f(-6)/4-(-6)

 

 

By the Mean Value Theorem, we know there exists a c in the open interval (-6, 4) 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(x) = 4 - 8x²

 

[f(4) - f(-6)]/[4 - (-6)] = [-124-(-284)]/10 = 16

 

Find c in the interval (-6, 4) so that f'(c) = 16

 

-16c = 16

 

     c = -1