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

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(C) Let $M = xy$. Given $x + y = 7$, we can write $y = 7 - x$. Substituting this into the expression for $M$, we get $M = x(7 - x) = 7x - x^2$. To fin

Vedclass · Accepted Answer

$\frac{49}{4}$

Vedclass · Answer

(C) Let $M = xy$. Given $x + y = 7$, we can write $y = 7 - x$. Substituting this into the expression for $M$, we get $M = x(7 - x) = 7x - x^2$. To find the maximum value, we differentiate $M$ with respect to $x$: $\frac{dM}{dx} = 7 - 2x$. Setting $\frac{dM}{dx} = 0$ for critical points, we get $7 - 2x = 0$, which implies $x = \frac{7}{2}$. Now, we find the second derivative: $\frac{d^2M}{dx^2} = -2$. Since $\frac{d^2M}{dx^2} The maximum value is $M = \frac{7}{2}(7 - \frac{7}{2}) = \frac{7}{2} 	imes \frac{7}{2} = \frac{49}{4}$.

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

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