extremum vs extremity

extremum and extremity both are nouns.

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

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

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