Definition:Point of Inflection/Definition 2
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Definition
Let $f$ be a real function which is differentiable on an interval $\Bbb I \subseteq \R$.
Let $\xi \in \Bbb I$.
$f$ 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 $\xi$.