define local maximum and minimum
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A function f has a local maximum or relative maximum at a point xo if the values f(x) of f for x 'near' xo are all less than f(xo). ... A function f has a local minimum or relative minimum at a point xo if the values f(x) of f for x 'near' xo are all greater than f(xo)
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The local maximum (also called the relative maximum) is the largest value of a function, given a certain range.
A local minimum is the lowest point on a function, given a certain range.
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