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Math Help - f(x) = xlnx. the minimum value attained by f is...

  1. #1
    Junior Member LexiRae's Avatar
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    f(x) = xlnx. the minimum value attained by f is...

    i think you do f'(x) and use the product rule?
    f'(x) = x (1/x) + lnx (1)
    1+lnx = 0
    lnx = -1

    ok i dont kow where to go from there.

    THANKS IN ADVANCE!
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    f'(x) = 1 + \ln{x} = 0

    \ln{x} = -1

    x = e^{-1} = \frac{1}{e}

    f'(x) = 1 + \ln{x}

    f''(x) = \frac{1}{x}

    f''(x) > 0 for all x in the domain of f(x), so f(x) is concave up everywhere, indicating f\left(\frac{1}{e}\right) is a minimum.

    value of the minimum is f\left(\frac{1}{e}\right) = -\frac{1}{e}
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