Explore BrainMass

Explore BrainMass

    Extreme value theorem

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    (Extreme Value Theorem) prove if f:K->R is continuous on a compact set K subset or equal to R, then f attains a maximum and minimum value.In other words there exists Xo,X1 belong to K such that f(Xo)<=f(X)<=f(X1) for all X belong to K.

    © BrainMass Inc. brainmass.com November 24, 2022, 11:54 am ad1c9bdddf

    Solution Preview

    To prove that f attains maximum and minimum, we need the following lemmas.

    Lemma 1: f:K->R continuous, K compact in R, F(K) is compact.

    Lemma 2: K subset of R is ...

    Solution Summary

    This is a proof regarding the extreme value theorem (maximum and minimum).