If x - 2y = 4, the minimum value of xy is - Vidyadip

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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