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JEE Main202226 Jun 2022Morning ShiftMathematicsApplication of DerivativesActual

The sum of the absolute minimum and the absolute maximum values of the function f x = 3 x - x 2 + 2 - x in the interval - 1 , 2 is

Options

  1. A17 + 3 2
  2. B17 + 5 2
  3. C5
  4. D9 - 17 2

Correct answer

A. 17 + 3 2

Step-by-step solution

Given f x = x 2 - 4 x - 2 , ∀ x ∈ - 1 , 3 - 17 2 - x 2 + 2 x + 2 , ∀ x ∈ [ 3 - 17 2 , 2 ) When x ∈ - 1 , 3 - 17 2 f ' x = 2 x - 4 = 0 ⇒ x = 2 Now f 2 = 2 , f - 1 = 3 f 3 - 17 2 = 17 - 3 2 When x ∈ [ 3 - 17 2 , 2 ) f ' x = - 2 x + 2 f ' x = - 2 x - 1 f ' x = 0 when x = 1 f 1 = 3 Hece, absolute minimum value = 17 - 3 2 and absolute maximum value = 3 Sum = 17 - 3 2 + 3 = 17 + 3 2

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