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Local maximum at x = −1− √ 15 /3, local minimum at x = −1+ √ 15 /3, global maximum at x = 2 and global minimum at x = −4. For a practical example, [ 6 ] assume a situation where someone has 200 {\displaystyle 200} feet of fencing and is trying to maximize the square footage of a rectangular enclosure, where x {\displaystyle x} is ...
The extreme value theorem was originally proven by Bernard Bolzano in the 1830s in a work Function Theory but the work remained unpublished until 1930. Bolzano's proof consisted of showing that a continuous function on a closed interval was bounded, and then showing that the function attained a maximum and a minimum value.
In mathematics, the maximum-minimums identity is a relation between the maximum element of a set S of n numbers and the minima of the 2 n − 1 non-empty subsets of S.
This is to be contrasted with the idea of global minimum (or global maximum), which corresponds to the minimum (resp., maximum) of the function across its entire domain. [ 2 ] [ 3 ] Properties of a single space
Stated precisely, suppose that f is a real-valued function defined on some open interval containing the point x and suppose further that f is continuous at x.. If there exists a positive number r > 0 such that f is weakly increasing on (x − r, x] and weakly decreasing on [x, x + r), then f has a local maximum at x.
The maximum of a subset of a preordered set is an element of which is greater than or equal to any other element of , and the minimum of is again defined dually. In the particular case of a partially ordered set , while there can be at most one maximum and at most one minimum there may be multiple maximal or minimal elements.
Then the effective domain of is denoted by and typically defined to be the set [1] [2] [3] = { : < +} unless is a concave function or the maximum (rather than the minimum) of is being sought, in which case the effective domain of is instead the set [2] = { : >}.
Is there an efficient way to find the global maximum/minimum? Take for example the sine integral. It has an infinite number of local maxima and minima. So how can one decide which one is the global maximum/minimum? --Abdull 17:04, 17 May 2007 (UTC) Not in the absolutely general case.