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f(x)=-8xlnx decreases over what domain

  • math - ,

    f'(x) = -8x(1/x ) + (-8)lnx
    = -8 - lnx
    to be decreasing, -8 - 8lnx < 0
    8lnx + 8 > 0
    8 lnx > -8
    lnx > -1

    (solve lnx = -1, x = 1/e

    which is true for all x > 1/e

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