Difference between revisions of "Extrema"
(New page: The upper and lower bounds of a real valued function are of interest in several situations in pure as well as applied Mathematics ==Absolute Extrema== Let <math>A</mat...) |
m |
||
Line 4: | Line 4: | ||
Let <math>A</math> be a set | Let <math>A</math> be a set | ||
− | Let <math>f:A\ | + | Let <math>f:A\rightarrow\mathbb{R}</math> |
Let the set <math>f(A)</math> be bounded | Let the set <math>f(A)</math> be bounded | ||
Line 20: | Line 20: | ||
<math>f(c)</math> is said to be a '''Local minimum''' iff <math>\exists\delta>0</math> such that <math>f(c)=\inf\{f(V_{\delta}(c))\}</math> | <math>f(c)</math> is said to be a '''Local minimum''' iff <math>\exists\delta>0</math> such that <math>f(c)=\inf\{f(V_{\delta}(c))\}</math> | ||
+ | |||
+ | ==See Also== | ||
+ | *[[Function]] | ||
+ | *[[Neighbourhoods]] | ||
+ | *[[Derivative]] | ||
+ | |||
+ | {{stub}} |
Latest revision as of 03:12, 15 February 2008
The upper and lower bounds of a real valued function are of interest in several situations in pure as well as applied Mathematics
Absolute Extrema
Let be a set
Let
Let the set be bounded
Then is called the Absolute or Global maximum of
and is called the Absolute or Global minimum of
Local Extrema
Let
Let
is said to be a Local maximum iff
such that
is said to be a Local minimum iff
such that
See Also
This article is a stub. Help us out by expanding it.