For x + y = 8,what is the maximum value of xy | vedclass

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(B) Given the constraint $x + y = 8$,we can express $y$ as $y = 8 - x$.Let the function to be maximized be $f(x) = xy$.Substituting $y$,we get $f(x) =

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$16$

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(B) Given the constraint $x + y = 8$,we can express $y$ as $y = 8 - x$.Let the function to be maximized be $f(x) = xy$.Substituting $y$,we get $f(x) = x(8 - x) = 8x - x^2$.To find the maximum value,we find the derivative $f'(x) = 8 - 2x$.Setting $f'(x) = 0$ for critical points,we get $8 - 2x = 0$,which implies $x = 4$.Since $x = 4$,then $y = 8 - 4 = 4$.The maximum value of $xy$ is $4 	imes 4 = 16$.

For $x + y = 8$,what is the maximum value of $xy$?

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