inflection point

A point where a curve switches from bending one way to bending the other.

An inflection point is a point on the graph of $f$ where concavity changes sign — $f''$ changes from positive to negative or vice versa. It must occur where $f''(x)=0$ or is undefined, though not every such point is actually an inflection point.

Examples

$f(x)=x^3$ has an inflection point at $x=0$ : $f''''(x)=6x$ is negative for $x<0$ and positive for $x>0$ .