Answer
If $a < 0$, then $\frac{2a}{3}$ is in the domain, and thus gives a critical point.
Work Step by Step
$f'(x) = \sqrt {x - a} + \frac{x}{{2\sqrt {x - a} }} = \frac{{2x - 2a + x}}{{2\sqrt {x - a} }} = \frac{{3x - 2a}}{{2\sqrt {x - a} }}$. This expression is zero when $x = \frac{2a}{3}$ , however, that number is not in the domain of $f$ if $a > 0$. However, if $a < 0$, then $\frac{2a}{3}$ is in the domain, and thus gives a
critical point.
