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

  • question_answer
    The maximum value of xy when \[x+2y=8\] is            [Kerala (Engg.) 2005]

    A)            20

    B)            16

    C)            24

    D)            8

    E)            4

    Correct Answer: D

    Solution :

               \[x+2y=8\], \[y=\frac{8-x}{2}\]                    Now \[f(x)=xy=x.\frac{(8-x)}{2}=4x-\frac{{{x}^{2}}}{2}\]                    \[\therefore \] \[{f}'(x)=4-x\]                    For extremum,\[{f}'(x)=0\]                    \[\therefore \] \[x=4\] and y = 2.                    Also \[{f}''(x)=-1<0\]                    So, maximum value of \[xy=4\times 2=8\].


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