If x + y = 10,then the maximum value of xy is | vedclass

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(C) Given $x + y = 10$,so $y = 10 - x$. Let $f(x) = xy = x(10 - x) = 10x - x^2$. To find the maximum value,we differentiate $f(x)$ with respect to $x$

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(C) Given $x + y = 10$,so $y = 10 - x$. Let $f(x) = xy = x(10 - x) = 10x - x^2$. To find the maximum value,we differentiate $f(x)$ with respect to $x$: $f'(x) = 10 - 2x$. Setting $f'(x) = 0$ for critical points: $10 - 2x = 0 \implies x = 5$. Now,find the second derivative to check for maxima: $f''(x) = -2$. Since $f''(5) = -2 Substituting $x = 5$ into $y = 10 - x$,we get $y = 5$. Therefore,the maximum value of $xy = 5 	imes 5 = 25$.

If $x + y = 10$,then the maximum value of $xy$ is

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