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STD 12 - 6. Application of derivatives — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 6. Application of derivatives1 Mark
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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