Passage: The calculus of variations is concerned with the maxima or minima (collectively called extrema) of functionals. A functional maps functions to scalars, so functionals have been described as "functions of functions."  Functionals have extrema with respect to the elements y of a given function space defined over a given domain. A functional J [ y ] is said to have an extremum at the function f   if ΔJ = J [ y ] − J [ f] has the same sign for all y in an arbitrarily small neighborhood of  f .  The function f is called an extremal function or extremal. The extremum J [ f ] is called a local maximum if ΔJ ≤ 0 everywhere in an arbitrarily small neighborhood of f , and a local minimum if ΔJ ≥ 0 there. For a function space of continuous functions, extrema of corresponding functionals are called weak extrema or strong extrema, depending on whether the first derivatives of the continuous functions are respectively all continuous or not.Both strong and weak extrema of functionals are for a space of continuous functions but weak extrema have the additional requirement that the first derivatives of the functions in the space be continuous.  Thus a strong extremum is also a weak extremum, but the converse may not hold.  Finding strong extrema is more difficult than finding weak extrema. An example of a necessary condition that is used for finding weak extrema is the Euler–Lagrange equation.

Question: What is another term for maxima?
extrema