extremum Math.
(ɛkˈstriːməm)
Pl. extrema, extremums.
[a. L. extrēmum, neut. of extrēmus (see extreme a., adv., and n.). First used as a mathematical term (in German) by P. du Bois-Reymond 1879, in Math. Ann. XV. 564.]
A value of a function that is a maximum or a minimum (either relative or absolute).
| 1904 O. Bolza Lect. Calculus Variations i. 10 The word ‘extremum’ will be used for maximum and minimum alike, when it is not necessary to distinguish between them. 1947 Courant & Robbins What is Math.? (ed. 4) vii. 343 A point where the derivative vanishes, whether it is an extremum or not, is called a stationary point. 1962 A. H. Frink tr. Akhiezer's Calculus of Variations i. 5 An extremum in the whole collection M is called an absolute extremum. We shall also consider relative extrema; to define them we must introduce the notion of neighbourhood. 1968 M. J. Forray Variational Calculus in Sci. & Engin. i. 6 Are f(4/5) = 44/55 and f(0) = 0 the absolute maximum and minimum for f(x) [= x4 - x5] in -2 {slle} x {slle} 2? We know that these extremums exist for a continuous function defined over a closed interval. |