Ichidan verb, Transitive verb
to carry to extremes; to go to the end of something; to reach the limits of something
多くの運動選手は青年時代に盛りを極める。Most athletes are at their best during their early manhood. to reach the peak of something (e.g. luxury, hardships, etc); to be extremely (e.g. busy)
to exhaust completely; to have nothing left (e.g. to say)
Also written 窮める【きわめる】