Explanation

(c)
$\because f(x) = \sqrt{ax} + \frac{a^{2}}{\sqrt{ax}}$
On differentiating w.r.t. $x$, we get
$f^{'}(x) = \frac{\sqrt{a}}{2\sqrt{x}} + \frac{a^{2}}{\sqrt{a}}\left( \frac{- 1}{2}x^{- 3/2} \right)$
$\Rightarrow f^{'}(x) = \frac{\sqrt{a}}{2\sqrt{x}} - \frac{a^{2}}{2\sqrt{a}}x^{- 3/2}$
$\therefore f^{'}(a) = \frac{\sqrt{a}}{2\sqrt{a}} - \frac{a^{2}}{2\sqrt{a}.a^{3/2}}$
$\Rightarrow f^{'}(a) = \frac{1}{2} - \frac{a^{2}}{2a^{2}} = 0$