If the function $f$ is continuous at $x = 3$, which of the following must be true?
(A) $f ( 3 ) < \lim _ { x \rightarrow 3 } f ( x )$
(B) $\lim _ { x \rightarrow 3 ^ { - } } f ( x ) \neq \lim _ { x \rightarrow 3 ^ { + } } f ( x )$
(C) $f ( 3 ) = \lim _ { x \rightarrow 3 ^ { - } } f ( x ) = \lim _ { x \rightarrow 3 ^ { + } } f ( x )$
(D) The derivative of $f$ at $x = 3$ exists.
(E) The derivative of $f$ is positive for $x < 3$ and negative for $x > 3$.