minimum vs extremum

minimum and extremum both are nouns.

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

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

Other hypernyms of minimum include peak, small indefinite amount, small indefinite quantity.

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

minimum (adjective)	extremum (adjective)
the least possible