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6. Application of derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
If $x - 2y = 4,$ the minimum value of $xy$ is
  • ✓
    $-2$
  • B
    $2$
  • C
    $0$
  • D
    $-3$
✓

Answer

Correct option: A.
$-2$
a
(a) $x - 2y = 4$ ==> $x = 2y + 4$ ……$(i)$

Let $P = xy$

From $(i),$ $P = y(2y + 4) = 4y + 2{y^2}$;

And $\frac{{dP}}{{dy}} = 4 + 4y = 0$

$y = - 1 \Rightarrow x = 2$ and $\frac{{{d^2}P}}{{d{y^2}}} = 4$(+ve)

$\therefore$ ${P_{{\rm{min}}{\rm{.}}}} = xy = (2)\,( - 1) = - 2$.

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