Let $f$ be a function that is twice differentiable on $- 2 < x < 2$ and satisfies the conditions in the table above. If $f ( x ) = f ( - x )$, what are the $x$-coordinates of the points of inflection of the graph of $f$ on $- 2 < x < 2$ ?
| \cline{2-3} \multicolumn{1}{c|}{} | $0 < x < 1$ | $1 < x < 2$ |
| $f ( x )$ | Positive | Negative |
| $f ^ { \prime } ( x )$ | Negative | Negative |
| $f ^ { \prime \prime } ( x )$ | Negative | Positive |
(A) $x = 0$ only
(B) $x = 1$ only
(C) $x = 0$ and $x = 1$
(D) $x = - 1$ and $x = 1$
(E) There are no points of inflection on $- 2 < x < 2$.