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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Increasing and Decreasing Function

  • question_answer
    The function \[f(x)=\frac{\log x}{x}\] is increasing in the interval                                                               [UPSEAT 2001]

    A)            \[(1,\,2e)\]

    B)            (0,e)

    C)            (2, 2e)

    D)            (1/e, 2e)

    Correct Answer: B

    Solution :

               \[f(x)=\frac{\log x}{x}\]            \[{f}'(x)=\frac{1}{{{x}^{2}}}-\frac{\log x}{{{x}^{2}}}=\frac{1-\log x}{{{x}^{2}}}\]            For \[f(x)\] to be increasing, \[{f}'(x)>0\]            Þ  \[1-\log x>0\] Þ \[1>\log x\] Þ \[e>x\]                    \\[f(x)\] is increasing in the interval \[(0,\,e)\].


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