Interactive Real Analysis

Let f be a function defined on a domain D, and c a point in D.

1. If there exists a neighborhood U of c with f(c) f(x) for all x in U, then f(c) is called a local maximum for the function f that occurs at x = c.
2. If there exists a neighborhood U of c with f(c) f(x) for all x in U, then f(c) is called a local minimum for the function f that occurs at x = c.
3. If f(x) has either a local minimum or a local maximum at x = c, then f(c) is called local extremum of the function f.