# Definition:Point of Inflection

## Definition

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

Let $\xi \in \Bbb I$.

### Definition 1

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

### Definition 2

$f$ has a **point of inflection at $\xi$** if and only if the derivative $f'$ of $f$ has either a local maximum or a local minimum at $\xi$.

## Also known as

A **point of inflection** can also be seen as **inflection point**.

An older spelling of **inflection** is **inflexion**.

Some sources give the term as a **flex**.