The minimum value of 2x + 3y, when xy = 6, is - Vidyadip

Question

The minimum value of $2x + 3y,$ when $xy = 6,$ is

✓

Answer

a
(a) $f(x) = 2x + 3y$ when $xy = 6$

$f(x) = 2x + 3y = 2x + \frac{{18}}{x}$

$f'(x) = 2 - \frac{{18}}{{{x^2}}} = 0$

==> $x = \pm 3$ and $f''(x) = \frac{{36}}{{{x^3}}} \Rightarrow f''(3) > 0$

Putting $x = + 3$, we get the minimum value to be $12.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If the equation ${\sin ^{ - 1}}\sqrt x + {\cos ^{ - 1}}\sqrt {{x^2} - 1} + {\tan ^{ - 1}}\left( {\tan \,y} \right) = a$ has at least one solution, then number of integral values of $a$ is

The length of the latus rectum of the parabola ${x^2} - 4x - 8y + 12 = 0$ is

If the period of the function $f(x) = \sin \left( {\frac{x}{n}} \right)$ is $4\pi $, then $n$ is equal to

How many numbers of five digits can be formed from the numbers $2, 0, 4, 3, 8$ when repetition of digits is not allowed

The number of permutations of the letters $a_1, a_2, a_3, a_4, a_5$ in which the first letter $a_1$ does not occupy the first position (from the left) and the second letter $a_2$ does not occupy the second position (from the left) is

Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}|=1,|\vec{b}|=4$ and $\vec{a} \cdot \vec{b}=2$. If $\vec{c}=(2 \vec{a} \times \vec{b})-3 \vec{b}$ and the angle between $\vec{b}$ and $\vec{c}$ is $\alpha$, then $192 \sin ^2 \alpha$ is equal to$........$

Let $S = \{ 0,\,1,\,5,\,4,\,7\} $. Then the total number of subsets of $S$ is

The value of ${(1 + i)^5} \times {(1 - i)^5}$ is

If $x, y, z \in R^+$ such that $x + y + z = 4$, then maximum possible value of $xyz^2$ is -

If the tangent at $\left( {1,7} \right)$ to the curve ${x^2} = y - 6$ touches the circle ${x^2} + {y^2} + 16x + 12y + c = 0$ then the value of $c$ is: