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Application of Derivatives question

2025 · Shift 2 · Q24

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PYQ Library
JEE Advanced
Mathematics
Application of Derivatives
2025 · Shift 2 · Q24

Application of Derivatives question

2025 · Shift 2 · Q24

JEE AdvancedMathematicsApplication of DerivativesMultiple correct+4 / −2

Let ℝ denote the set of all real numbers. Let f: ℝ → ℝ be defined by

f(x) = \begin{cases} \dfrac{6x + \sin x}{2x + \sin x}, & \text{if } x eq 0, \\ \dfrac{7}{3}, & \text{if } x = 0. \end{cases}

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

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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