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

  • question_answer
    If \[x+y=10\], then the maximum value of xy is

    A)            5

    B)            20

    C)            25

    D)            None of these

    Correct Answer: C

    Solution :

               \[x+y=10;\]\[\therefore y=10-x\]                                 ?..(i)            Now \[f(x)=xy=x(10-x)=10x-{{x}^{2}}\]            \[\therefore f'(x)=10-2x\]                    For maximum value of \[f(x),\,f'(x)=0\]                    \[\therefore x=5\] and \[y=5\]                    So maximum value of \[xy=5\times 5\,\,=25\].


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