Minimiarvon

Minimiarvo is a mathematical concept used to denote the smallest value that a quantity can take within a given context, such as a function, a set, or a data sample. The term is used across disciplines including mathematics, statistics, and applied sciences. In Finnish, minimiarvon is the genitive form of minimiarvo, and appears in phrases like “minimiarvon määrittäminen” (determination of the minimum value).

In mathematics, the minimum value of a function f on a domain D is the smallest value that f(x) attains for x in D. If such a value exists, it may be global (the smallest over the entire domain) or local (the smallest within a neighborhood of a point). The input that yields the minimum is called a minimizer or argmin. Common methods to locate minima include calculus techniques, such as solving f'(x) = 0 and checking second derivatives, and examining endpoints when the domain is closed and bounded.

In discrete settings and statistics, the minimum often refers to the smallest element in a finite collection. For example, the minimum of a set {a, b, c} is min(a, b, c). In statistics, the sample minimum is the smallest observed value in a dataset and can be used in describing dispersion (along with the maximum) and in computing the range.

Noting the linguistic usage, minimiarvon-form is employed in Finnish texts to express possession or relation, as in “minimiarvon vaikutus.”