Let $\mathbb { R }$ denote the set of all real numbers. Define the function $f : \mathbb { R } \rightarrow \mathbb { R }$ by

$$f ( x ) = \left\{ \begin{array} { c c } 
2 - 2 x ^ { 2 } - x ^ { 2 } \sin \frac { 1 } { x } & \text { if } x \neq 0 \\
2 & \text { if } x = 0
\end{array} \right.$$

Then which one of the following statements is TRUE?

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\begin{tabular}{|l|l|}
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(A) & The function $f$ is NOT differentiable at $x = 0$ \\
\hline
(B) & There is a positive real number $\delta$, such that $f$ is a decreasing function on the interval ( $0 , \delta$ ) \\
\hline
(C) & For any positive real number $\delta$, the function $f$ is NOT an increasing function on the interval ( $- \delta , 0$ ) \\
\hline
(D) & $x = 0$ is a point of local minima of $f$ \\
\hline
\end{tabular}
\end{center}