Point of local extremum among integers - Revision history

Vipul: Created page with "==Definition== Suppose $f$ is a function whose domain of definition contains an integer $n$ as well as the integers $n - 1$ and $n + 1$
2012-06-04T17:34:48Z

Created page with "==Definition== Suppose <math>f</math> is a function whose domain of definition contains an integer <math>n</math> as well as the integers <math>n - 1</math> and <math>n + 1</..."

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==Definition==

Suppose <math>f</math> is a function whose domain of definition contains an integer <math>n</math> as well as the integers <math>n - 1</math> and <math>n + 1</math>. We say that <math>n</math> is a '''point of local extremum among integers''' for <math>f</math> if it is either a point of local maximum among integers or a point of local minimum among integers Both notions are defined below.

===Point of local maximum among integers===

We say that <math>n</math> is a point of local maximum among integers for <math>f</math> if <math>f(n) \ge f(n - 1)</math> and <math>f(n) \ge f(n + 1)</math>.

===Point of local minimum among integers===

We say that <math>n</math> is a point of local minimum among integers for <math>f</math> if <math>f(n) \le f(n - 1)</math> and <math>f(n) \le f(n + 1)</math>.