Terminology
If f 0(x0) = 0, we say that x0 is a stationary number of f . However, if f 00(x0) = 0, we do not have a specific name for x0.
For local extremizers, there are two types: local maximizers and local minimizers. Correspondingly, there are also two types of inflection numbers. However, we do not have specific names to distinguish the two types.