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AP EAMCET · Maths · Application of Derivatives

The number of turning points of the curve \(f(x)=2 \cos x-\sin 2 x\) in the interval \([-\pi, \pi]\) is

  1. A \(4\)
  2. B \(3\)
  3. C \(1\)
  4. D \(2\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(3\)

Step-by-step Solution

Detailed explanation

\(f'(x) = \frac{d}{dx}(2 \cos x - \sin 2x) = -2 \sin x - 2 \cos 2x\) \(f'(x) = 0 \Rightarrow -2 \sin x - 2 \cos 2x = 0\) \(\sin x + \cos 2x = 0\) \(\sin x + (1 - 2\sin^2 x) = 0\) \(2\sin^2 x - \sin x - 1 = 0\) \((2\sin x + 1)(\sin x - 1) = 0\) \(\sin x = 1\) or…