Question

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

• A. $-2$
• B. $0$
• C. $1$
• D. $-3$

Answer 1

The correct option is A $-2$

Let $t=xy$

substituting $x$ from $\left(i\right)$

$t=(4+2y)yt=2y^2+4y$

At minimum value of $t$

$\frac{dt}{dy}=0\frac{d}{dy}(2y^2+4y)=0\Rightarrow 4y+4=0\Rightarrow y=-1$

$\Rightarrow t=(4+2y)y$

$\Rightarrow t=(4-2)(-1)=-2$

So minimum value is $-2$

Option $A$ is correct.