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JEE Main2018MathematicsApplication of DerivativesActual

Let f x = x 2 + 1 x 2 and g x = x - 1 x , x ∈ R - - 1 , 0 , 1 . If h x = f x g x , then the local minimum value of h x is:

Options

  1. A2 2
  2. B3
  3. C- 3
  4. D- 2 2

Correct answer

A. 2 2

Step-by-step solution

f x = x 2 + 1 x 2 = x - 1 x 2 + 2 g x = x - 1 x x ∈ R - - 1 , 0 , 1 Let x - 1 x = t h x = f x g x = t 2 + 2 t = t + 2 t t ∈ R - 0 h x = t + 2 t A M ≥ G M Minimum of h x ⇒   t + 2 t 2   ≥   t × 2 t t + 2 t ≥ 2 2 Local minimum = 2 2

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