Question

determine the points of inflection of the function
f(x) = x + sin(x)

Answer 1

f'(x)=1+ cos(x)

Answer 2

f''(x)=-sin(x)

Answer 3

find where f'' is 0
then you can check to see if the concavity switches but we know it does here at each time f''=0

Answer 4

-sin(x)=0

true when x=0, pi

Answer 5

in general
\[x=npi, n \in \mathbb{Z} \]