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BITSAT2017MathematicsApplication of DerivativesActual

The maximum value of f ( x ) = x + sin 2 x , x ∈ [ 0 , 2 π ] is

Options

  1. Aπ 2
  2. B2 π
  3. C3 π 4
  4. D3 π 2

Correct answer

B. 2 π

Step-by-step solution

Given, f x = x + sin 2 x ⇒   f ' ( x ) = 1 + 2 cos 2 x For maximum or minimum value, f ' x = 0 ⇒   1 + 2 cos 2 x = 0 ⇒ cos 2 x = - 1 2 ⇒   2 x = 2 n π ± 2 π 3 ⇒   x = n π ± π 3 ⇒   x = π 3 , 2 π 3 , 4 π 3 , 5 π 3 Find f 0 ,   f π 3 , f 2 π 3 ,   f 4 π 3 ,   f 5 π 3 ,   f ( 2 π ) ⇒   f 0 = 0 , f π 3 = π 3 + 3 2 , f 2 π 3 = 2 &#96

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