peak: [16] Peak seems to come ultimately from the noun pick ‘pointed implement’ (as in toothpick). From this in the 15th century was formed an adjective picked ‘pointed’, which survived dialectally into the 19th century (S H A Hervey noted in the Wedmore Chronicle 1887 ‘Children still use ‘picked’ of a pencil with a good point to it’). It had a variant form peaked, from which peak appears to have been derived as a back-formation. The adjective peaky ‘sickly’ [19], incidentally, is not etymologically related. It comes from a now little used verb peak ‘become sickly or pale’ [16], whose origins are unknown. => pick
peak (n.)
"pointed top," 1520s, variant of pike (n.4) "sharp point." Meaning "top of a mountain" first recorded 1630s, though pike was used in this sense c. 1400. Figurative sense is 1784. Meaning "point formed by hair on the forehead" is from 1833. According to OED, The Peak in Derbyshire 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; 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 highest point" first recorded 1958. Related: peaked; peaking.