Divide 10 into two parts such that the sum of | vedclass

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

Question

(D) Let $x$ and $y$ be the two parts of the number $10$. $	herefore x + y = 10 \implies y = 10 - x$ ... $(i)$ Let $A$ be the sum of double of the fir

Vedclass · Accepted Answer

$(9, 1)$

Vedclass · Answer

(D) Let $x$ and $y$ be the two parts of the number $10$. $	herefore x + y = 10 \implies y = 10 - x$ ... $(i)$ Let $A$ be the sum of double of the first and the square of the second: $A = 2x + y^2$ Substituting $y = 10 - x$ into the equation: $A = 2x + (10 - x)^2$ $A = 2x + 100 - 20x + x^2$ $A = x^2 - 18x + 100$ To find the minimum,differentiate $A$ with respect to $x$: $\frac{dA}{dx} = 2x - 18$ Set $\frac{dA}{dx} = 0$ for critical points: $2x - 18 = 0 \implies x = 9$ Check the second derivative: $\frac{d^2A}{dx^2} = 2$. Since $2 > 0$,the function has a minimum at $x = 9$. Substitute $x = 9$ into $(i)$: $y = 10 - 9 = 1$. Thus,the parts are $(9, 1)$.

Divide $10$ into two parts such that the sum of double of the first and the square of the second is minimum.

Similar Questions

If $y = a \ln x + bx^2 + x$ has its extremum value at $x = 1$ and $x = 2,$ then $(a, b) =$

The radius of the cylinder of maximum volume,which can be inscribed in a sphere of radius $R$ is

The function $f(x) = x^2 + \frac{54}{x}$

Let $f(x) = 1 + 2x^2 + 2^2x^4 + \dots + 2^{10}x^{20}$. Then $f(x)$ has:

Vedclass Test Series

Exam Paper Generator

Online Exam Module