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  • Need clarity, kindly explain! The maximum value of xy subject to x+y=8, is

The maximum value of xy subject to x+y=8, is

  • Option 1)

    8

  • Option 2)

    16

  • Option 3)

    20

  • Option 4)

    24

 

Answers (1)

best_answer

x+y=8\\ P=xy=x(8-x)\\ P=8x-x^{2}\\ \frac{dp}{dx}=8-2x=0\\ \therefore x=4\\ \therefore y=4\\ \therefore xy=4\times 4=16


Option 1)

8

This solution is incorrect 

Option 2)

16

This solution is correct 

Option 3)

20

This solution is incorrect 

Option 4)

24

This solution is incorrect 

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