Definition:Point of Inflection/Definition 1

Definition
Let $f$ be a real function which is differentiable on an interval $\Bbb I \subseteq \R$.

Let $\xi \in \Bbb I$.

$f$ has a point of inflection at $\xi$ $\xi$ is a point on $f$ at which $f$ changes from being concave to convex, or vice versa.

Also see

 * Equivalence of Definitions of Point of Inflection