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AP EAMCET202023 Sep 2020Morning ShiftMathematicsApplication of DerivativesActual

The difference between the greatest and least values of the function f ( x ) = - x + sin 2 x on - π 2 , π 2 is

Options

  1. A3 + 2 ?
  2. B3 + 2 2 + π 6
  3. Cπ 2 + π 2
  4. D3 2 - π 6

Correct answer

C. π 2 + π 2

Step-by-step solution

f ( x ) = - x + sin 2 x in - π 2 , π 2 f ' ( x ) = 2 cos 2 x - 1 = 0 ⇒ x = ± π 6 f ( x ) increasing in x ∈ - π 6 , π 6 decreasing in x ∈ - π 2 , - π 6 ∪ π 6 , π 2 f ( x ) maximum at x = - π 2 or π 6 f - π 2 = π 2 f ( x ) minimum at x = π 2 f π 2 = - π 2 So, π 2 + π 2 = π

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