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

  • question_answer
    The maximum value of xy subject to \[x+y=8\], is                    [MNR 1995]

    A)            8

    B)            16

    C)            20

    D)            24

    Correct Answer: B

    Solution :

               \[x+y=8;\]\[\therefore y=8-x\]                      .....(i)                Now \[f(x)=xy=x(8-x)=8x-{{x}^{2}}\], \[\therefore {f}'(x)=8-2x\]                    For maximum value of \[f(x),\,f'(x)=0\]                    \[\therefore \] \[x=4\] and \[y=4\]                    So, maximum value of \[xy=4\times 4=16\].


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