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

  • question_answer
    Let \[y={{x}^{2}}{{e}^{-x}}\], then the interval in which y increases with respect to x is [MNR 1994; Kurukshetra CEE 1998]

    A)            \[(-\infty ,\infty )\]

    B)            \[(-2,\,0)\]

    C)            \[(2,\infty )\]

    D)            \[(0,\,2)\]

    Correct Answer: D

    Solution :

               \[\frac{dy}{dx}=\frac{-1}{{{e}^{x}}}x(x-2)\] is \[+ve\]when \[x(x-2)\]is \[-ve\] i.e., x lies in the interval (0, 2), exponential function as we know is always \[+ve\].


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