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$f (x) = \sin x + \cos 2 x (x > 0)$ has minima at $x =$

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$(2 n + 1) \frac{π}{2}, \forall n \in Z$

$\frac{n π}{2}, \forall n \in Z$

$n π, \forall n \in Z$

answer is A.

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Detailed Solution

$f^{1} (x) = \cos x - 2 \sin 2 x \Rightarrow f^{1} (x) = 0 \Rightarrow x = \frac{π}{2}, \frac{3 π}{2} . . .$

$At x = \frac{π}{2}, \frac{3 π}{2}, f^{11} (x) > 0 .$

$f (x) is minimum at x = (2 n + 1) \frac{π}{2}$

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