Question

Find the average value of f(x) on the interval [-1, 3] when f'(x)=3x^2-6x and f(2)=0.

Answer 1

the average value of f(x) on [a,b] is

∫[a,b] f(x) dx
-----------------------
b-a

f' = 3x^2-6x
f = x^3-3x^2+4

so, you want

∫[-1,3] x^3-3x^2+4 dx
--------------------------
3 - (-1)

which I'm sure you can do.