Let : R" be a continuous map. Assume that lim||||-→∞ f(x) = 0 and that f(zo) > 0 for some to ER". Show that there exists z* ER" such that achieves its global maximum at z*.
Let : R" be a continuous map. Assume that lim||||-→∞ f(x) = 0 and that f(zo) > 0 for some to ER". Show that there exists z* ER" such that achieves its global maximum at z*.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:8. Let
that
that
: R" be a continuous map. Assume that lim||||→∞ √(x) = 0 and
(ro) > 0 for some ro ER". Show that there exists * ER" such
achieves its global maximum at z*.
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