peak vs extremum

peak and extremum both are nouns.

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

As nouns, extremum is a hypernym of peak; that is, extremum is a word with a broader meaning than peak:

Other hypernyms of peak include extreme, extreme point.

As nouns, peak and extremum are synonyms defined as:

peak (noun)	extremum (noun)
a brim that projects to the front to shade the eyes	the point located farthest from the middle of something
the top or extreme point of something (usually a mountain or hill)	the most extreme possible amount or value
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

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