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

  • question_answer
    The interval in which the function \[{{x}^{2}}{{e}^{-x}}\]is non decreasing, is

    A)            \[(-\infty ,\,\,2]\]

    B)            [0, 2]

    C)            \[[2,\,\,\infty )\]

    D)            None of these

    Correct Answer: B

    Solution :

               Let \[y=f(x)={{x}^{2}}{{e}^{-x}}\]                    Þ \[\frac{dy}{dx}=2x{{e}^{-x}}-{{x}^{2}}{{e}^{-x}}={{e}^{-x}}(2x-{{x}^{2}})\]                    Hence \[f'(x)\ge 0\] for every \[{{e}^{ax}}[a\cos (bx+c)-b\sin (bx+c)]\]therefore it is non-decreasing in [0,2].


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