Extreme Value Theorem: If function [math]f[/math] is continuous on a closed interval [math][a,b][/math], then [math]f[/math] attains absolute maximum value [math]f(c)[/math] and an absolute minimum value [math]f(d)[/math] at some numbers [math]c[/math] and [math]d[/math] in [math][a,b][/math].