Explanation

(a)
Given, $x - 2y = 4$
Let $A = xy\ \ \ \Rightarrow \ \ \ \ A = 2y^{2} + 4y$
$\Rightarrow \ \ \ \frac{dA}{dy} = 4 + 4y$
For extremum value, $\frac{dA}{dy} = 0$
$\Rightarrow \ \ \ \ \ y = - 1$
Now, $\frac{d^{2}A}{dy^{2}} = 4 > 0$, minima
At $y = - 1$,
$x = 4 + 2( - 1) = 2$
$\therefore\ \ \ \ A = xy = 2( - 1) = - 2$
$\therefore$ Minimum value of $xy$ is $- 2$