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Definition 6.5.11: Local Extremum

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.
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