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JEE Main202226 Jun 2022Morning ShiftMathematicsApplication of DerivativesActual

Let f x = 2 cos - 1 x + 4 cot - 1 x - 3 x 2 - 2 x + 10 , x ∈ - 1 , 1 . If a , b is the range of the function, then 4 a - b is equal to

Options

  1. A11
  2. B11 - π
  3. C11 + π
  4. D15 - π

Correct answer

B. 11 - π

Step-by-step solution

Given f x = 2 cos - 1 x + 4 cot - 1 x - 3 x 2 - 2 x + 10 f ' x = - 2 1 - x 2 - 4 1 + x 2 - 6 x - 2 = - 2 1 1 - x 2 + 2 1 + x 2 + 3 x + 1 f ' x < 0   ⇒ f x is a decreasing function Now f 1 = π + 5 and f - 1 = 5 π + 5 So, range: a , b ≡ π + 5 , 5 π + 5 a = π + 5 ,   b = 5 π + 5 ⇒ 4 a - b = 11 - π

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