interior point

A point strictly between the two ends of an interval, not sitting on either edge.

An interior point of a closed interval $[a,b]$ is any point strictly between the endpoints, $a < x < b$ — as opposed to an endpoint, $x=a$ or $x=b$ . The distinction matters for locating extrema: Fermat's Theorem (a critical point at a local extremum) only applies at interior points, since an endpoint has no "both sides" to compare.

Examples

On $[-2,3]$ , the point $x=0$ is interior; $x=-2$ and $x=3$ are endpoints, not interior points.