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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Maxima and Minima

  • question_answer
    A minimum value of \[\int_{0}^{x}{t{{e}^{-{{t}^{2}}}}}\]dt  is       [EAMCET 2003]

    A)            1

    B)            2

    C)            3

    D)            0

    Correct Answer: D

    Solution :

               \[f(x)=\int_{0}^{x}{t{{e}^{-{{t}^{2}}}}}dt\Rightarrow f'(x)=x{{e}^{-{{x}^{2}}}}=0\Rightarrow x=0\]            \[{f}''(x)={{e}^{-{{x}^{2}}}}(1-2{{x}^{2}});\ \ \ {f}''\,(0)=1>0\]                    \[\therefore \] Minimum value \[f(0)=0\].


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