extremity vs extremum

extremity and extremum both are nouns.

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

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

Other hyponyms of extremity include bound, boundary, bounds, end, terminal, extreme, extreme point, limit.

extremity (noun)	extremum (noun)
an external body part that projects from the body	the point located farthest from the middle of something
that part of a limb that is farthest from the torso	the most extreme possible amount or value
the outermost or farthest region or point
the greatest or utmost degree
an extreme condition or state (especially of adversity or disease)