Let $\mathbb{R}$ denote the set of all real numbers. Define the function $f: \mathbb{R} \rightarrow \mathbb{R}$ by
$$
f(x)=\left\{\begin{array}{cc}
2-2 x^2-x^2 \sin \frac{1}{x} & \text { if } x \neq 0 \\
2 & \text { if } x=0
\end{array}\right.
$$
Then which one of the following statements is TRUE?
