Extrems

Extrems is a nonstandard or informal term used to refer to extrema, the extreme values of a function, a data set, or a phenomenon. In mathematics, extrema are points where a function reaches its largest or smallest value on a given domain. Local (or relative) extrema are points where the function is higher or lower than nearby points, whereas global (or absolute) extrema are the maximum or minimum over the entire domain. For many functions, extrema are found among critical points—points where the derivative is zero or undefined. Classification as a maximum or minimum can be obtained via the second derivative test, the first derivative test, or other criteria.

In optimization, locating extrema means identifying input values that maximize or minimize an objective function, subject to any constraints. In discrete data, extrema describe the largest and smallest observed values, though they may be affected by sampling and outliers. In statistics, the term extremes may also describe tail behavior or extreme value theory, which studies the probabilistic behavior of maxima and minima of random samples.

Usage notes: extrems is not standard in formal writing; extrema or extreme values are preferred. The term extrema originates from Latin extremus and is used across calculus, analysis, and optimization. Related concepts include supremum and infimum, which generalize global maxima and minima to sets that may not attain their extreme values.