Mean Value Theorem and Average Slope help?

Question

Let 𝑓(𝑥)=2𝑥²+5𝑥−8

1) Find the average slope of the function 𝑓 on the interval [−1,1]

2) Verify the Mean Value Theorem by finding a number 𝑐 in (−1,1) such that 𝑓′(𝑐)=𝑚

I got 3 for the average slope is that not right? I can't figure out the second part.

Answer 1

1) Average slope m = [f(1) - f(- 1)]/(1 - (- 1)] = (- 1 + 11)/2 = 5

2) f'(x) = 4x + 5; f'(c) = 4c + 5 = 5; 4c = 0; c = 0

Answer 2

Substitute 3 for f'(x) and solve for x.