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If x+y is constant, prove that xy is maximum when x=y . Please answer the above problem as soon as possible.

If x+y is constant, prove that xy is maximum when x=y.
 
Please answer the above problem as soon as possible.

Grade:11

2 Answers

Susmita
425 Points
5 years ago
Let x+y=c
Or,y=c-x
So xy=x(c-x)=cx-x2
Take derivative of xy wrt x.
d(xy)/dx=d(cx-x2)/dx=c-2x
For xy to be minimum,
c-2x=0
Or,x=c/2
Putting it in y=c-x we get
y=c/2.
So x=y
If it helps please approve.
 
Susmita
425 Points
5 years ago
That would be maximum in place of minimum.
You can essily check maxima condition by
d2(xy)/dx2=d(c-2x)/dx=-2
You can also  write x=c-y and take derivative of xy wrt y.You will arrive at the same result.
 

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