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JEE Main20208 Jan 2020Morning ShiftMathematicsApplication of DerivativesActual

Let f x = x cos - 1 ⁡ - sin ⁡ x , x ∈ - π 2 , π 2 , then which of the following is true?

Options

  1. Af ' is increasing in - π 2 , 0 and decreasing in 0 , π 2
  2. Bf ' 0 = - π 2
  3. Cf is not differentiable at x = 0
  4. Df ' is decreasing in - π 2 , 0 and increasing in 0 , π 2

Correct answer

D. f ' is decreasing in - π 2 , 0 and increasing in 0 , π 2

Step-by-step solution

f ' x = x π - c o s - 1 s i n x = x ( π π 2 - s i n - 1 s i n x = x π 2 + x f x = x π 2 + x x ≥ 0 x π 2 - x x < 0 f ' x = π 2 + 2 x x ≥ 0 π 2 - 2 x x < 0 f ' x is increasing in 0 ,   π 2 and decreasing in - π 2 ,   0 .

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