extreme point vs vertex

extreme point and vertex both are nouns.

Word	Noun	Adjective	Verb	Adverb
extreme point	Yes	No	No	No
vertex	Yes	No	No	No

As nouns, vertex is a hyponym of extreme point; that is, vertex is a word with a more specific, narrower meaning than extreme point:

Other hyponyms of extreme point include acme, apex, peak.

extreme point (noun)	vertex (noun)
the point located farthest from the middle of something	the point of intersection of lines or the point opposite the base of a figure
	the highest point (of something)