peak vs extreme point

peak and extreme point both are nouns.

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

As nouns, extreme point is a hypernym of peak; that is, extreme point is a word with a broader meaning than peak:

Other hypernyms of peak include extreme, extremum.

peak (noun)	extreme point (noun)
a brim that projects to the front to shade the eyes	the point located farthest from the middle of something
the top or extreme point of something (usually a mountain or hill)
the highest point (of something)
the most extreme possible amount or value
a V shape
the highest level or degree attainable; the highest stage of development
the period of greatest prosperity or productivity

peak (verb)	extreme point (verb)
to reach the highest point; attain maximum intensity, activity