MATH 1151 Lecture Notes - Lecture 21: Maxima And Minima
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A function ! has a global maximum (also called an absolute maximum) at " = $ if, for all other " in its domain, ! " In this case, ! ($) is called the maximum value of !. A function ! has a global minimum (also called an absolute minimum) at " = $ if, for all other " in its domain, ! " In this case, ! ($) is called the minimum value of !. The maximum and minimum values are called the extreme values of the function. A function ! has a local maximum (also called a relative maximum) at " = ), if ! " ()) for every " in some open interval * containing ). A function ! has a local minimum (also called a relative minimum) at " = ), if ! " ()) for every " in some open interval * containing.