A peak is (1) a maximum, (2) to achieve a maximum, and (3) to bring to a maximum.
Its homophone pique, which appears mostly in the phrase pique [one's] interest, means (1) to provoke or arouse, or (2) to provoke resentment or indignation. It also works as a noun referring to a feeling of resentment or indignation resulting from wounded pride.
A third homophone, peek, means (1) to glance quickly, (2) to look furtively, or (3) a quick or furtive look.
It peaked with Della famously being photographed dancing to I Will Survive in a skin-tight red dress. [Daily Mail]
The unexpected availability of an experienced playmaker as soon as next month is sure to pique the interest of NRL clubs. [Sydney Morning Herald]
Like a sneak peek into old age, I grunt when I bend and climb stairs in slow motion. [Globe and Mail]