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Extreme value theorem

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(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.

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Solution Summary

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

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 ...

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