What does extrema mean?
"Extrema" is the plural of "extremum" and denotes the points at which a function reaches its greatest or least value — its maxima and minima. The term belongs primarily to mathematics and its applied sciences: in calculus, finding extrema is a classic technique that involves setting a function's derivative to zero to locate peaks, valleys, and turning points. Mathematicians distinguish local (or relative) extrema, which are the highest or lowest points within a neighborhood, from global (or absolute) extrema, which are the true extremes across an entire domain. Beyond pure mathematics, the word appears in physics, engineering, statistics, and climatology wherever the outer bounds of a measured quantity matter, such as the extrema of a temperature record. Derived from Latin extremus, meaning "utmost" or "outermost," it carries a precise, technical register rather than an everyday one, making it essential vocabulary for students of calculus but uncommon elsewhere.
nounExtrema are the points at which a function attains a maximum or minimum value — the highest and lowest values in a given range or domain. The word is the plural of "extremum" and is used chiefly in mathematics.
- In mathematics, the maximum and minimum values of a function over a given interval or domain (local/relative extrema versus global/absolute extrema).
- By extension, the most extreme points or conditions of any measurable system, such as the highest and lowest temperatures on record.
"To locate the function's extrema, set the derivative equal to zero and solve for x."
"The graph shows two local extrema within the interval from zero to pi."
"Climatologists examined the extrema of the temperature record to assess how heat waves have shifted."
"Extrema" is itself the plural of "extremum" and should not be given a further plural. In practice, writers often treat it as a collective noun referring to all maxima and minima together.
"The theorem guarantees that a continuous function on a closed interval attains both of its extrema."
Every rollercoaster's highest peak and deepest dip can be found with calculus: those thrill-points are the ride's extrema.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of extrema
"Extrema" derives from the Latin adjective extremus, the superlative of exterus, meaning "outer" or "outward"; extremus thus meant "outermost" or "utmost." English borrowed the related word "extreme" directly from this Latin root, and "extremum" was later adopted as a mathematical term for a point of maximum or minimum value, with "extrema" as its plural. The same Latin lineage gives English other words such as "extremity" and "extremely," all sharing the core sense of reaching the outermost limit.
Related word forms
How extrema is actually used
"Extrema" is a technical term used almost exclusively in mathematics, physics, engineering, and data analysis; it is rarely encountered in everyday conversation. It functions as the plural of "extremum", though in practice many writers use it as a collective term for all maxima and minima of a function without reference to the singular form.
Easily confused with extrema
"Extreme" refers to something very great in degree or far from the ordinary, while "extrema" specifically names the maximum and minimum points of a function.
"Extremity" means the outermost or farthest point (or a limb of the body), whereas "extrema" denotes the high and low values in mathematics.