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BCECE Engineering BCECE Engineering Solved Paper-2011

  • question_answer
    The function \[{{x}^{x}}\]decreases in the interval

    A)  (0, e)                                     

    B)         (0, 1)                     

    C)          (0, 1/e)                                

    D)         None of these

    Correct Answer: C

    Solution :

    Let \[f(x)={{x}^{x}}\] \[f(x)={{x}^{x}}[1+\log x]={{x}^{x}}(\log e+\log x)\] \[={{x}^{x}}(\log ex)\]                 Put \[f(x)=0\Rightarrow {{x}^{x}}(\log ex)=0\]                 \[\Rightarrow \]    \[x=0,1/e\] Hence, function decreases in the interval \[(0,1/e).\]


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