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Let f be continuous on a closed interval. then f assumes its minimum and maximum values....

Let f be continuous on a closed interval. then f assumes its minimum and maximum values. Hint Construct a squence(xn) for which (f(xn) converges to the supremum M of f, apply the Bolzano-Weierstrass theorem to get a convergent subsequence of (xn), and invoke the continuity of f at the limit of that convergent subsequence. (Extreme Value Theorem)

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