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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2015

  • question_answer
    The function\[\frac{2}{3}\]increases in the interval

    A) (4. 5)      

    B) (0,2)       

    C) (2.3)       

    D) (3, 4)

    Correct Answer: B

    Solution :

    Given.\[f(x)={{x}^{2}}{{e}^{-x}}\] On differentiating both sides w.r.t.\[x,\]we get. \[f'(x)=2x{{e}^{-x}}-{{x}^{2}}{{e}^{-x}}\] For\[f(x)\] to be increasing,\[f'(x)>0\] \[\Rightarrow \]               \[2x{{e}^{-x}}-{{x}^{2}}{{e}^{-x}}>0\] \[\Rightarrow \]               \[{{e}^{-x}}x(2-x)>0\] \[\therefore \]  \[x\in (0,2)\]


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