Consider the function f(x) = 2x^3 - 3x^2 - 72x + 6 on the interval [-5,8]. Find the average or mean slope of the function on this interval, & (see description)

Question

Consider the function f(x) = 2x^3 - 3x^2 - 72x + 6 on the interval [-5,8].

A) Find the average or mean slope of the function on this interval.

B) By the Mean Value Theorem, we know there exists a c in the open interval (-5,8) such that f′(c) is equal to this mean slope. For this problem, there are two values of c that work.

1. The smaller one is __
2. The larger one is __

Answer 1

[f(8) - (f(-5) / (8 - (-5)) = m

f'(c) = m

Can you solve for c and answer?