The maximum value of xy subject to x+y=7 is | vedclass

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(C) Let $M = xy$. Given $x+y = 7$,so $y = 7-x$. Substituting $y$ in $M$,we get $M = x(7-x) = 7x - x^2$. To find the maximum value,differentiate $M$ wi

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$\frac{49}{4}$

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(C) Let $M = xy$. Given $x+y = 7$,so $y = 7-x$. Substituting $y$ in $M$,we get $M = x(7-x) = 7x - x^2$. To find the maximum value,differentiate $M$ with respect to $x$: $\frac{dM}{dx} = 7 - 2x$. For critical points,set $\frac{dM}{dx} = 0$,which gives $7 - 2x = 0$,so $x = \frac{7}{2}$. Now,find the second derivative: $\frac{d^2M}{dx^2} = -2$. Since $\frac{d^2M}{dx^2} The maximum value is $M = \frac{7}{2}(7 - \frac{7}{2}) = \frac{7}{2}(\frac{7}{2}) = \frac{49}{4}$.

The maximum value of $xy$ subject to $x+y=7$ is

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