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5 November, 11:12

Maximum value of (log x) / x

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  1. 5 November, 11:44
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    Y = log x / x

    y ' = ((log x) ' * x - (x) ' * log x) / x²=

    = (1/x * x - 1 * log x) / x² =

    = (1 - log x) / x²

    y ' = 0;

    1 - log x = 0

    log x = 1

    x = e

    The maximum value:

    y max = log e / e = 1 / e
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