Show that the function $f(x) = \frac{x}{3} - \sqrt{x}$ satisfies the conditions of Rolle's Theorem on $[0, 9]$.
(i) $\frac{x}{3}$ is continuous on $\mathbb{R}$, therefore $\frac{x}{3}$ continuous on $[0, 9]$. $\sqrt{x}$ is continuous on $[0, \infty)$, therefore $\sqrt{x}$ continuous on $[0, 9]$. Hence, $f(x) = \frac{x}{3} - \sqrt{x}$ continuous on $[0, 9]$.
(ii) $f'(x) = $ for $x \neq $, therefore $f(x)$ is differentiable on $(0, 9)$.
(iii) $f(0) = $; $f(9) = $ therefore $f(0) \text{?} f(9)$.
Find all numbers $c$ that are guaranteed by the theorem. (Enter your answers as a comma-separated list.)
C =
