# For what values of x does the graph of f have a horizontal tangent f(x)=x+2sinx?

Dec 16, 2016

$x = \frac{2 \pi}{3} , \frac{4 \pi}{3}$, in the interval 0 ≤ x ≤2pi

#### Explanation:

Start by differentiating.

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

The derivative represents the instantaneous rate of change of the function. A horizontal tangent will have a $0$ slope. Therefore, we set the derivative to $0$ and solve.

$0 = 1 + 2 \cos x$

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

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

Hopefully this helps!