# What are the points of inflection of f(x)=x+sinx  on the interval x in [0,2pi]?

May 27, 2018

${x}_{1} = 0$ or ${x}_{2} = \pi$ or ${x}_{3} = 2 \cdot \pi$

#### Explanation:

We have
$f \left(x\right) = x + \sin \left(x\right)$
Then
$f ' \left(x\right) = 1 + \cos \left(x\right)$
$f ' ' \left(x\right) = - \sin \left(x\right)$
Solving $\sin \left(x\right) = 0$ for $x$in the given interval we get
$x = 0$
$x = \pi$
$x = 2 \pi$