# How do you find the critical numbers of f(x) = x + 2sinx?

Nov 26, 2016

The critical points are $x = \frac{4 \pi}{3} + 2 \pi n \mathmr{and} \frac{2 \pi}{3} + 2 \pi n$

#### Explanation:

The derivative of the function is

$f ' \left(x\right) = 1 + 2 \cos x$

Critical points will occur whenever the derivative equals $0$ or is undefined.

$0 = 1 + 2 \cos x$

$- 1 = 2 \cos x$

$- \frac{1}{2} = \cos x$

$x = \frac{4 \pi}{3} + 2 \pi n \mathmr{and} \frac{2 \pi}{3} + 2 \pi n$

Hopefully this helps!