Extreme Value Theorem
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If the function is continuous over the closed interval , then there is at least one maximum value (green) and one minimum value (red) of in that interval.
Contributed by: Jacqueline Wandzura (March 2011)
Additional contributions by: Stephen Wandzura
Open content licensed under CC BY-NC-SA
Snapshot 3: If a function is monotone increasing or decreasing in a given interval, then the endpoints must be the extrema.
"Extreme Value Theorem"
Wolfram Demonstrations Project
Published: March 7 2011