maximal vs maximum

maximal is not a noun while maximum is a noun.

Word	Noun	Adjective	Verb	Adverb
maximal	No	Yes	No	No
maximum	Yes	Yes	No	No

As adjectives, maximal and maximum are synonyms defined as:

maximal (noun)	maximum (noun)
	the greatest possible degree
	the point on a curve where the tangent changes from positive on the left to negative on the right
	the largest possible quantity

maximal (adjective)	maximum (adjective)
the greatest or most complete or best possible	the greatest or most complete or best possible