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

$$f ( x ) = \begin{cases} \frac { 6 x + \sin x } { 2 x + \sin x } & \text { if } x \neq 0 \\ \frac { 7 } { 3 } & \text { if } x = 0 \end{cases}$$

Then which of the following statements is (are) TRUE?

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(A) & The point $x = 0$ is a point of local maxima of $f$ \\
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(B) & The point $x = 0$ is a point of local minima of $f$ \\
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(C) & Number of points of local maxima of $f$ in the interval $[ \pi , 6 \pi ]$ is 3 \\
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(D) & Number of points of local minima of $f$ in the interval $[ 2 \pi , 4 \pi ]$ is 1 \\
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\end{tabular}
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