Etymology
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peak (n.)

1520s, "pointed top, projecting summit," a variant of pike (n.4) "sharp point." Meaning "top of a mountain, a precipitous mountain with a more or less conical summit" is recorded by 1630s, though pike was used in this sense c. 1400. Figurative sense is 1784. Of beards, 1590s; of hats, 1650s. Meaning "point formed by hair on the forehead" is from 1833. As "the highest point" in any varying quantity, or the time when this occurs, by 1902. 

The Peak, the prominent hill in Derbyshire, England, is older than the word for "mountaintop;" compare Old English Peaclond, for the district, Pecsaetan, for the people who settled there, Peaces ærs for Peak Cavern. In this case it is sometimes said to be a reference to an elf-denizen Peac "Puck."

peak (v.)

1570s, "to rise in a peak," from peak (n.). Figurative meaning "reach the highest point" is recorded by 1958. Related: peaked; peaking.

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Definitions of peak
1
peak (n.)
the most extreme possible amount or value;
voltage peak
Synonyms: extremum
peak (n.)
the period of greatest prosperity or productivity;
peak (n.)
the highest level or degree attainable; the highest stage of development;
the peak of perfection
summer was at its peak
Synonyms: acme / height / elevation / pinnacle / summit / superlative / meridian / tiptop / top
peak (n.)
the top or extreme point of something (usually a mountain or hill);
the view from the peak was magnificent
Synonyms: crown / crest / top / tip / summit
peak (n.)
a V shape;
Synonyms: point / tip
peak (n.)
the highest point (of something);
at the peak of the pyramid
Synonyms: vertex / apex / acme
peak (n.)
a brim that projects to the front to shade the eyes;
Synonyms: bill / eyeshade / visor / vizor
2
peak (v.)
to reach the highest point; attain maximum intensity, activity;
That wild, speculative spirit peaked in 1929
Synonyms: top out
From wordnet.princeton.edu