AP CALCULUS
posted by Kasie .
Using the mean value theorem;
F'(x) = f(b)f(a) / ba
f(x)=x^28x+3; interval [1,6]

I assume you want to find c such that f'(c) = (f(6)f(1))/7
nothing simpler:
f'(x) = 2x8
f(6) = 9
f(1) = 12
so, we want f'(c) = 21/7 = 3
2x8 = 3
x = 5/2