Multiple Choice Questions on The maximum value of ln x x is ........ for NDA Exam Preparation

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Multiple Choice Questions

The maximum value of ln x x is ........

Mathematics (NDA) Diffrentiation
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    The maximum value of ln x / x is -

    e

    Incorrect Answer

    1 / e

    Correct Answer

    2 / e

    Incorrect Answer

    1

    Incorrect Answer
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    Explanation:

    let y = ln x / x 

    y’ = 1−ln x / x2 

    y’’ = −(3−2 lnx) / x3

    Put y’ = 0 implies that x = e

    y’’(e) = −1 / e3 < 0

    ∴ Maxima will be at x = e

    Now max value = y(e) = ln / e = 1 / e

    By: Yachna
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