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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$\frac{49}{4}$

Vedclass · Answer

(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

Similar Questions

$A$ bimetallic strip consists of metals $X$ and $Y$. It is mounted rigidly at the base as shown in the figure. The metal $X$ has a higher coefficient of linear expansion compared to that of metal $Y$. When the bimetallic strip is placed in a cold bath, what happens?

The peculiarity of sponges is

$\int_0^1 \sin \left(2 \tan ^{-1} \sqrt{\frac{1+x}{1-x}}\right) d x$ is equal to :

If the slope of one line is twice the slope of the other in the pair of straight lines $ax^2 + 2hxy + by^2 = 0$,then $8h^2$ is equal to (in $ab$)

The functional kidney of a frog tadpole is

Vedclass Test Series

Exam Paper Generator

Online Exam Module