(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 March 4, 2021, 6:05 pm ad1c9bdddf
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 ...
This is a proof regarding the extreme value theorem (maximum and minimum).