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

Application of Derivatives

Section: Mathematics

Question : 1 of 32

Marks: +1, -0

Let R denote the set of all real numbers. Let f:R⟶R be defined by
f(x)={

‌

6x+sin‌x

2x+sin‌x

‌ if ‌x≠0

‌

‌ if ‌x=0

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

[JEE Adv 2025 P2]

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