A) Find the average value of

Question

f(x)=x^3-x+1 on the interval (0,2)
B) Find c so that f(c)equals the average value

Answer 1

avg value is area divided by width, so
1/2 ∫[0,2] x^3-x+1 dx
= 2

So, since the area is 4, and the width is 2, a rectangle of height 2 will have the same area.

We need to solve

f(x) = 2
x^3-x+1 = 2
x^3-x-1 = 0
x = 1.32