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JEE Main202125 Jul 2021Morning ShiftMathematicsApplication of DerivativesActual

Let f x = 3 sin 4 x + 10 sin 3 x + 6 sin 2 x - 3 , x ∈ - π 6 , π 2 . Then, f is :

Options

  1. Aincreasing in - π 6 , π 2
  2. Bdecreasing in 0 , π 2
  3. Cincreasing in - π 6 , 0
  4. Ddecreasing in - π 6 , 0

Correct answer

D. decreasing in - π 6 , 0

Step-by-step solution

f x = 3 sin 4 x + 10 sin 3 x + 6 sin 2 x - 3 ,   x ∈ - π 6 , π 2 ⇒ f ' x = 12 sin 3 x cos x + 30 sin 2 x cos x + 12 sin x cos x = 6 sin x cos x 2 sin 2 x + 5 sin x + 2 = 6 sin x cos x ( 2 sin x + 1 ) ( sin x + 2 ) From wavy curve, we can say f ' ( x ) < 0 in - π 6 , 0 So, the function is Decreasing in - π 6 , 0

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