Let $\mathbb{R}$ denote the set of all real numbers. Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by
$
f(x)=\left\{\begin{array}{cc}
\frac{6 x+\sin x}{2 x+\sin x} & \text { if } x \neq 0 \\
\frac{7}{3} & \text { if } x=0
\end{array}\right.
$
Then which of the following statements is (are) TRUE?
Select ALL correct options:
A
The point $x=0$ is a point of local maxima of $f$
B
The point $x=0$ is a point of local minima of $f$
C
Number of points of local maxima of $f$ in the interval $[\pi, 6 \pi]$ is 3
D
Number of points of local minima of $f$ in the interval $[2 \pi, 4 \pi]$ is 1
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