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AIEEE 2002

JEE Main 2002 Mathematics question on Application of Derivatives

The length of a longest interval in which the function 3sin⁡x−4sin⁡3x3\sin x - 4\sin^3 x is increasing, is
  1. A.
    π3\dfrac{\pi}{3}
  2. B.
    π2\dfrac{\pi}{2}
  3. C.
    3π2\dfrac{3\pi}{2}
  4. D.
    π\pi
Show answer and solution

Correct option: A

Solution

3sinx − 4sin³x = sin3x. This is increasing when cos3x > 0, i.e., 3x ∈ (−π/2 + 2kπ, π/2 + 2kπ), so x ∈ (−π/6 + 2kπ/3, π/6 + 2kπ/3). Each such interval has length (π/6) − (−π/6) = π/3.

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