If x + y = 8,find the maximum value of xy. | vedclass

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(B) Let $z = xy$.Given $x + y = 8$,we have $y = 8 - x$.Substituting $y$ in $z$,we get $z = x(8 - x) = 8x - x^2$.To find the maximum value,we different

Vedclass · Accepted Answer

$16$

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(B) Let $z = xy$.Given $x + y = 8$,we have $y = 8 - x$.Substituting $y$ in $z$,we get $z = x(8 - x) = 8x - x^2$.To find the maximum value,we differentiate $z$ with respect to $x$:$\frac{dz}{dx} = 8 - 2x$.Setting $\frac{dz}{dx} = 0$,we get $8 - 2x = 0$,which implies $x = 4$.Now,find the second derivative: $\frac{d^2z}{dx^2} = -2$.Since $\frac{d^2z}{dx^2} Substituting $x = 4$ into the equation for $y$,we get $y = 8 - 4 = 4$.The maximum value is $z = xy = 4 	imes 4 = 16$.

If $x + y = 8$,find the maximum value of $xy$.

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