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JCECE Engineering JCECE Engineering Solved Paper-2014

  • 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 :

    Given,\[x+y=10\]                 \[y=10-x\]                                           ... (i) Now,\[f(x)=xy=x(10-x)=10x-{{x}^{2}}\] \[\therefore \]  \[f'(x)=10-2x\] For maximum value of\[f(x)\], put\[f'(x)=0\] \[\Rightarrow \]               \[10-2x=0\Rightarrow x=5\] \[\therefore \]  \[x=5\]and\[y=5\][from Eq. (i)] Hence, maximum value of\[xy=5\times 5=25\]


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