Unformatted text preview: x, f ( x )) is a local minimum if there is an interval ( a, b ) with a < x < b and f ( x ) ≤ f ( z ) for every z in ( a, b ). A local extremum is either a local minimum or a local maximum. Local maximum and minimum points are quite distinctive on the graph of a function, and are therefore useful in understanding the shape of the graph. In many applied problems we want to ﬁnd the largest or smallest value that a function achieves (for example, we might want to ﬁnd the minimum cost at which some task can be performed) and so identifying maximum and minimum points will be useful for applied problems as well. Some examples of local maximum and minimum points are shown in ﬁgure 5.1 . 93...
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 Fall '07
 JonathanRogawski
 Math, Calculus, Critical Point, Optimization, Fermat's theorem

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