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

  • question_answer
    If \[x-2y=4,\] the minimum value of \[xy\] is [UPSEAT 2003]

    A)            ? 2

    B)            2

    C)            0

    D)            ? 3

    Correct Answer: A

    Solution :

               \[x-2y=4\] Þ  \[x=2y+4\]                        ??(i)            Let \[P=xy\]            From (i), \[P=y(2y+4)=4y+2{{y}^{2}}\]; \[\frac{dP}{dy}=4+4y=0\]            \[y=-1\Rightarrow x=2\] and \[\frac{{{d}^{2}}P}{d{{y}^{2}}}=4\](+ve)            \ \[{{P}_{\text{min}\text{.}}}=xy=(2)\,(-1)=-2\].


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