extremum vs maximum

extremum and maximum both are nouns.

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

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

Other hyponyms of extremum include lower limit, minimum, upper limit.

extremum (noun)	maximum (noun)
the point located farthest from the middle of something	the greatest possible degree
the most extreme possible amount or value	the point on a curve where the tangent changes from positive on the left to negative on the right
	the largest possible quantity

extremum (adjective)	maximum (adjective)
	the greatest or most complete or best possible