extremum vs peak

extremum and peak both are nouns.

Word	Noun	Adjective	Verb	Adverb
extremum	Yes	No	No	No
peak	Yes	No	Yes	No

As nouns, peak is a hyponym of extremum; that is, peak is a word with a more specific, narrower meaning than extremum:

Other hyponyms of extremum include acme, apex, vertex.

As nouns, extremum and peak are synonyms defined as:

extremum (noun)	peak (noun)
the point located farthest from the middle of something	a brim that projects to the front to shade the eyes
the most extreme possible amount or value	the top or extreme point of something (usually a mountain or hill)
	the highest point (of something)
	the most extreme possible amount or value
	a V shape
	the highest level or degree attainable; the highest stage of development
	the period of greatest prosperity or productivity

extremum (verb)	peak (verb)
	to reach the highest point; attain maximum intensity, activity