Verified Solution • 2025–26 Session moderate

QJEEM24Ma9f8d: JEE Main 2024 Mathematics - Class 12 JEEM24Ma9f8d Solution: Let . The number of points of local maxima of in interval is

Let f(x)=4cos⁡3x+33cos⁡2x−10f(x)=4 \cos ^3 x+3 \sqrt{3} \cos ^2 x-10 . The number of points of local maxima of ff in interval (0,2π)(0,2 \pi) is

Multiple Choice Options

  • A 1
  • B 3
  • C 4
  • D 2

Step-by-Step Verified Solution

amp;f(x)=4cos⁡3x+33cos⁡2x−10amp;f′(x)=12cos⁡2x⋅(−sin⁡x)+63cos⁡x⋅(−sin⁡x)=0amp;=−63cos⁡x⋅sin⁡x(1+23cos⁡x)=0amp;cos⁡x=0,sin⁡x=0,cos⁡x=−32\begin{aligned}& f(x)=4 \cos ^3 x+3 \sqrt{3} \cos ^2 x-10 \\& f^{\prime}(x)=12 \cos ^2 x \cdot(-\sin x)+6 \sqrt{3} \cos x \cdot(-\sin x)=0 \\& =-6 \sqrt{3} \cos x \cdot \sin x\left(1+\frac{2}{\sqrt{3}} \cos x\right)=0 \\& \cos x=0, \sin x=0, \cos x=\frac{-\sqrt{3}}{2}\end{aligned}

Sign of f(x)f(x)

JEE Main 2024 (Online) 8th April Morning Shift Mathematics - Application of Derivatives Question 13 English Explanation

∴ Maxima at 5π6,7π6\therefore \text { Maxima at } \frac{5 \pi}{6}, \frac{7 \pi}{6}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring