"the greatest amount, quantity, or degree," 1740, from French maximum and directly from Latin maximum (plural maxima), neuter of maximus "greatest," which is superlative of magnus "great, large, big" (of size), "abundant" (of quantity), "great, considerable" (of value), "strong, powerful" (of force); of persons, "elder, aged," also, figuratively, "great, mighty, grand, important," from PIE *mag-samo-, superlative form of root *meg- "great."
<a href="https://www.etymonline.com/word/maxi-">Etymology of maxi- by etymonline</a>
Harper, D. (n.d.). Etymology of maxi-. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/maxi-