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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.
Let x+y=cOr,y=c-xSo xy=x(c-x)=cx-x2Take derivative of xy wrt x.d(xy)/dx=d(cx-x2)/dx=c-2xFor xy to be minimum,c-2x=0Or,x=c/2Putting it in y=c-x we gety=c/2.So x=yIf it helps please approve.
That would be maximum in place of minimum.You can essily check maxima condition byd2(xy)/dx2=d(c-2x)/dx=-2You can also write x=c-y and take derivative of xy wrt y.You will arrive at the same result.
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