(above the second) non-zero derivative to be of odd order (third, fifth, etc.). If the lowest-order non-zero derivative is of even order, the point is not a point of inflection, but an undulation point. However, in algebraic geometry, both inflection points and undulation points are usually called inflection points. An example of an undulation point is for the function given by .

In the preceding assertions, it is assumed that has some higher-order non-zero derivative at , which is not necessarily the case. If it is the case, the condition