Unformatted text preview: a and b , and we want to know the largest or smallest value that f ( x ) takes on, not merely values that are the largest or smallest in a small interval. That is, we seek not a local maximum or minimum but a global maximum or minimum, sometimes also called an absolute maximum or minimum. Any global maximum or minimum must of course be a local maximum or minimum. If we ﬁnd all possible local extrema, then the global maximum, if it exists , must be the largest of the local maxima and the global minimum, if it exists , must be the smallest of the local minima. We already know where local extrema can occur: only at those points at which f ± ( x ) is zero or undeﬁned. Actually, there are two additional points at which a 105...
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 Spring '07
 JonathanRogawski
 Math, Calculus, Derivative, Optimization, maximum

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