Consider the following statement:
(*) If $f ( x )$ is an integer for every integer $x$, then $f ^ { \prime } ( x )$ is an integer for every integer $x$.
Which one of the following is a counterexample to (*)?
A $f ( x ) = \frac { x ^ { 3 } + x + 1 } { 4 }$
B $f ( x ) = \frac { x ^ { 4 } + x ^ { 2 } + x } { 2 }$
C $f ( x ) = \frac { x ^ { 4 } + x ^ { 3 } + x ^ { 2 } + x } { 2 }$
D $f ( x ) = \frac { x ^ { 4 } + 2 x ^ { 3 } + x ^ { 2 } } { 4 }$