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

  • question_answer
    The minimum value of \[2x+3y,\] when \[xy=6,\] is [MP PET 2003]

    A)            12

    B)            9

    C)            8

    D)            6

    Correct Answer: A

    Solution :

               \[f(x)=2x+3y\] when \[xy=6\]            \[f(x)=2x+3y=2x+\frac{18}{x}\]                \[{f}'(x)=2-\frac{18}{{{x}^{2}}}=0\]            Þ \[x=\pm 3\] and  \[{f}''(x)=\frac{36}{{{x}^{3}}}\Rightarrow {f}''(3)>0\]                    Putting \[x=+3\],  we get the minimum value to be 12.


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