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 $xy = 6$
(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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