The sum of two numbers is fixed. Then their p | vedclass

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

Question

(A) Let the two numbers be $x$ and $y$.Given that their sum is fixed,let $x + y = s$,where $s$ is a constant.Then $y = s - x$.Let the product be $f(x)

Vedclass · Accepted Answer

Each number is half of the sum

Vedclass · Answer

(A) Let the two numbers be $x$ and $y$.Given that their sum is fixed,let $x + y = s$,where $s$ is a constant.Then $y = s - x$.Let the product be $f(x) = xy = x(s - x) = sx - x^2$.To find the maximum product,we differentiate $f(x)$ with respect to $x$:$f'(x) = s - 2x$.Setting $f'(x) = 0$ for critical points:$s - 2x = 0 \Rightarrow x = s/2$.Since $f''(x) = -2 Substituting $x = s/2$ into $y = s - x$,we get $y = s - s/2 = s/2$.Thus,the product is maximum when each number is half of the sum.

The sum of two numbers is fixed. Then their product is maximum when:

Similar Questions

The maximum volume (in $m^3$) of the right circular cone having slant height $3 \, m$ is

If $m$ and $M$ respectively denote the minimum and maximum of $f(x)=(x-1)^2+3$ for $x \in [-3, 1]$, then the ordered pair $(m, M)$ is equal to

Let a rectangle $ABCD$ of sides $2$ and $4$ be inscribed in another rectangle $PQRS$ such that the vertices of the rectangle $ABCD$ lie on the sides of the rectangle $PQRS$. Let $a$ and $b$ be the sides of the rectangle $PQRS$ when its area is maximum. Then $(a+b)^2$ is equal to :

The minimum value of the function $f(x) = x \log x$ is

Let the radius and height of a right circular cylinder be related as $r^2 + h = 6$. If the volume of the cylinder is maximum,then the value of $\frac{r}{h}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module