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?
Select the correct option:
A
The function $f$ is NOT differentiable at $\mathrm{x}=0$
B
There is a positive real number $\delta$, such that $f$ is a decreasing function on the interval $(0, \delta)$
C
There is a positive real number $\delta$, such that $f$ is a decreasing function on the interval $(0, \delta)$
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