$f (x) = s i n x + cos 2 x (x > 0)$ has minima at $x$

(2 n + 1) \frac{π}{2}

\forall n \in Z

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\frac{n π}{2}, \forall n \in Z

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n π, \forall n \in Z

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\frac{n π}{4}, \forall n \in Z

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Solution

The correct option is B $(2 n + 1) \frac{π}{2}$ ,
$\forall n \in Z$
$f^{1} (x) = c o s x - 2 s i n^{2} x$
$f^{1} (x) = c o s x (1 - 2 s i n x)$
$f^{1} (x) > 0$ If $0 < x < \frac{π}{6}$
$f^{1} (x) < 0$ If $\frac{π}{6} < x < \frac{π}{2}$
$f^{1} (x) > 0$ If $\frac{π}{2} < x < \frac{5 π}{6}$
$f^{1} (x) < 0$ If $\frac{5 π}{6} < x < \frac{3 π}{2}$
$f^{1} (x) > 0$ $\frac{3 π}{2} < x < \frac{13 π}{6}$
$f^{1} (x) = 0$ If $x = (2 n + 1) \frac{π}{2}$ & $(4 n + 1) \frac{π}{6}$
& minima occur at $x = (2 n + 1) \frac{π}{2}$

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