Definition:Point of Inflection
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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.
Also see
- Results about points of inflection can be found here.
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {II}$. Calculus: Differentiation: Maximum, Minimum and Point of Inflection