JEE Main 2024 Mathematics question
Let f(x) = 4cos³x + 3√3 sin²x − 10. The number of points of local maxima of f in interval (0, 2π) is:
Answer: (B)
Solution
f′(x) = −12cos²x sin x + 6√3 sin x cos x = −6 sin x cos x(2cos x − √3). f′ changes from + to − at x = π/2 and x = 3π/2 (local maxima); the point x = π/6 gives
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