Definition:Point of Inflection/Definition 2

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 $\xi$ the derivative $f'$ of $f$ has either a local maximum or a local minimum at $\xi$.

Also see

 * Equivalence of Definitions of Point of Inflection