Let R denote the set of all real numbers. Let f: R \rightarrow R be defined by f(x)= \{ \begin{array}{c}\\\{6 x+ \sin \\\x\end\frac{array}{2 x+ \sin x} , \text{ if } x \neq 0 ; \frac{7}{3} , \text{ if } x=0} Then which of the following statements is (are) TRUE? [JEE Adv 2025 P2]

The point x=0 is a point of local maxima of f

The point x=0 is a point of local minima of f

Number of points of local maxima of f in the interval [\pi, 6 \pi] is 3

Number of points of local minima of f in the interval [2 \pi, 4 \pi] is 1

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Application of Derivatives

Section: Mathematics

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