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## Extrema on Compact Sets |

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z | overview |

Let be a continuous real multivariate function defined on a compact set (i.e.the set is bounded and closed). Then has a minimum and a maximum on In other words there exist a maximum point such that for all and a minimum point with for all

Note that there may exist more than one maximum point and more than one minimum point.

The picture shows the graph of a function of two variables with several extrema. On the right hand side the corresponding level curves are shown.

automatically generated 1/23/2017 |