maximum

—maximumly, adv.

/mak"seuh meuhm/, n., pl. maximums, maxima /-meuh/, adj.

n.

1. the greatest quantity or amount possible, assignable, allowable, etc.

2. the highest amount, value, or degree attained or recorded.

3. an upper limit allowed or allowable by law or regulation.

4. Math.

a. Also called relative maximum, local maximum. the value of a function at a certain point in its domain, which is greater than or equal to the values at all other points in the immediate vicinity of the point. Cf. absolute maximum.

b. the point in the domain at which a maximum occurs.

adj.

5. that is a maximum; greatest or highest possible or attained: maximum satisfaction; maximum temperature.

6. pertaining to a maximum or maximums.

[1730-40; < L, n. use of neut. of maximus, superl. of magnus great, large]

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In mathematics, a point at which a function's value is greatest.

If the value is greater than or equal to all other function values, it is an absolute maximum. If it is merely greater than any nearby point, it is a relative, or local, maximum. In calculus, the derivative equals zero or does not exist at a function's maximum point. Techniques for finding maximum and minimum points motivated the early development of calculus and have made it easier to solve problems such as finding the dimensions of a container that will hold the most for a given amount of material used to make it. See also minimum, optimization.

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