We introduce the Extreme Value Theorem, which states that if f is a continuous function on a closed interval [a,b], then f takes on a maximum f(c) and a minimum f(d) at points c and d in the interval [a,b]. We also discuss critical points/critical numbers and their importance to finding extreme values. We then look at several examples of continuous and discontinuous functions where the EVT does and doesn't apply. We finish with a basic set of Extreme Value Theorem problems.

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