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

  • Calculus - ,

    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

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