Answer

f (x) = sin x

The first derivative is f '(x) = cos x and the second derivative is

f "(x) = -sin x.

The second derivative is never undefined, and is zero at nπ for every integer n. Therefore our inflection points are nπ for every integer n. If we look at the graph, this makes sense. We can think of the graph of sin x as a series of upside down and right-side up bowls, and an inflection point occurs between every two bowls: