HW Supplement: Extreme Value Theorem Name 1. A closed interval, [a,b] includes or excludes the endpoints? 2. What are the two hypotheses of the Extreme Value Theorem? If f(x) is on a interval, then. 3. The Extreme Value Theorem guarantees absolute extrema when those two hypotheses hold. Where do we find the extrema? a. or b. 4. The function f(x): 1 == does NOT have an absolute maximum on the interval [-1,1]. Why not? x 5. Use the Extreme Value Theorem to find the extrema of f(x)=x³ +3x² +7 on [-3,2] Do not use a graphing utility. Demonstrate application of the theorem.

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