Let f(x)=4x−−√−4x for x>0. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relativ

Question

Let f(x)=4x−−√−4x for x>0. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima).

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Ivy 3 weeks 2021-10-01T11:48:31+00:00 1 Answer 0

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    2021-10-01T11:50:29+00:00

    Answer:

    Explanation:

    f(x) = ∫πy²dx = ∫π(4x – √-4x)² = ∫π(16x² – 8x√-4x + 4x)dx

    Divide through by 4x: f(x) = ∫π(4x -2√-4x + 1)dx limit (0,1)

    = π{2x² + 1/4(-4x)^1/2 + x) limit (0,1)

    = π( 2 + 1/8 + 1)  = π(25/8) = 3.125π

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