Question

Using the mean value theorem;
F'(x) = f(b)-f(a) / b-a

f(x)=x^2-8x+3; interval [-1,6]

Answer 1

I assume you want to find c such that f'(c) = (f(6)-f(-1))/7

nothing simpler:

f'(x) = 2x-8
f(6) = -9
f(-1) = 12

so, we want f'(c) = -21/7 = -3
2x-8 = -3
x = 5/2