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

MCQ

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

✓
$12$
B
$9$
C
$8$
D
$6$

✓

Answer

Correct option: A.

$12$

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 $12.$

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