Definition: Local Extremum

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.

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