Extremum

An extremum is a maximum or minimum. An extremum may be local (a.k.a. a relative extremum; an extremum in a given region which is not the overall maximum or minimum) or global. Functions with many extrema can be very difficult to graph.

Notorious examples include the functions  and  near , plotted above.

Another pathological example is  near 0 and 1, which has

extrema in the closed interval [0,1] (Mulcahy 1996).

REFERENCES:

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 14, 1972.

Mulcahy, C. "Plotting and Scheming with Wavelets." Math. Mag. 69, 323-343, 1996.

Tikhomirov, V. M. Stories About Maxima and Minima. Providence, RI: Amer. Math. Soc., 1991.