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
![|_(e^(11))/pi-1/2_|-[(e^9)/pi-1/2]+1=19058-2579+1=16480](https://mathworld.wolfram.com/images/equations/Extremum/NumberedEquation1.svg){kind=small}
extrema in the closed interval [0,1] (Mulcahy 1996).
See also
Global Extremum, Global Maximum, Global Minimum, Kuhn-Tucker Theorem, Lagrange Multiplier, Local Extremum, Local Maximum, Local Minimum, Maximum, Minimum
Explore with Wolfram|Alpha
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.
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Extremum." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Extremum.html