Find the average value of the function over the given interval and all values of x in the interval for which the function = its avg value?

(Round your answer to three decimal places.)

f(x) = 4x^3 − 3x^2,   [−1, 2]

1 Answer

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  • 2 months ago

    average of f = (1/(2– –1))∫(4x³ − 3x²)dx between –1 and 2

    average of f = (1/3)(x⁴ − x³) between –1 and 2

    average of f = (1/3)((2⁴ − 2³) – ((–1)⁴ − (–1)³))

    average of f = (1/3)((16 − 8) – (1 + 1))

    average of f = (1/3)(8 – 2) = 2

    4x³ − 3x² = 2

    solve for x

    graphically, about 1.13

    Attachment image
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