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NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

The function f x = tan ⁡ x + 1 x ,   ∀ x ∈ 0 , π 2 has

Options

  1. Aone local maximum
  2. Bone local minimum
  3. Cone local maximum and one minimum
  4. Dno local maximum or minimum

Correct answer

B. one local minimum

Step-by-step solution

d y d x = sec 2 ⁡ x – 1 x 2 = x - cos ⁡ x x + cos ⁡ x cos 2 ⁡ x . x 2 Hence, at α sign of d y d x changes from negative to positive i.e., y = f x has a local minimum

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