# Infection point

Introduction: A function is not necessarily convex or concave on the entire domain. A function can be convex on parts of the domain, and concave on the other parts of the domain.

Definition: A point of the domain where the function changes from convex to concave (or from concave to convex) is called an inflection point.

Remark: From the second-order condition it follows that for an inflection point it holds that $y''(x)=0$.