Mathematics

Question

h(x)= 1/8x^3-x^2

What is the average rate of change of h over the interval −2≤x≤2?

1 Answer

  • Answer:

    [tex]\frac{1}{2}[/tex]

    Step-by-step explanation:

    The average rate of change of h(x) in the closed interval [ a, b ] is

    [tex]\frac{f(b)-f(a)}{b-a}[/tex]

    Here [a, b ] = [ - 2, 2 ], thus

    f(b) = f(2) = [tex]\frac{1}{8}[/tex] × 2³ - 2² = 1 - 4 = - 3

    f(a) = [tex]\frac{1}{8}[/tex] × (- 2)³ - (- 2)² = - 1 - 4 = - 5

    average rate of change = [tex]\frac{-3-(-5)}{2-(-2)}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

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