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maximum

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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maximum

1. Maths

a. a value of a function that is greater than any neighbouring value

b. a stationary point on a curve at which the tangent changes from a positive value on the left of this point to a negative value on the right

c. the largest number in a set

2. Astronomy

a. the time at which the brightness of a variable star has its greatest value

b. the magnitude of the star at that time

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maximum [′mak·sə·məm]

(mathematics)

The maximum of a real-valued function is the greatest value it assumes. Abbreviated max.