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JEE Main20206 Sep 2020Evening ShiftMathematicsApplication of DerivativesActual

The set of all real values λ for which the function f x = 1 - cos 2 x . λ + sin x , xε - π 2 , π 2 , has exactly one maxima and exactly one minima, is :

Options

  1. A- 1 2 ,   1 2 - 0
  2. B- 3 2 ,   3 2
  3. C- 1 2 ,   1 2
  4. D- 3 2 ,   3 2 - 0

Correct answer

D. - 3 2 ,   3 2 - 0

Step-by-step solution

f x = sin 2 x λ + sin x f ' x = sin x cos x 2 λ + 3 sin x sin x = 0 (one point) sin x = - 2 λ 3 ∈ - 1 , 1 - 0 .....(1) λ ∈ - 3 2 , 3 2 - 0

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