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Final review - Harvard University Math 20 Fall 2011...

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Harvard University, Math 20 Fall 2011, Instructor: Rachel Epstein 1 Review for Final Exam You should review all the material for the midterms, as well as the following new material below. 1. Optimization without constraints (Chapter 17.4-9): (a) Know what a stationary point is and that these are the only possible interior points that are (local or global) extreme points. (b) Know and use the second-derivative test (Theorem 17.5), which helps to determine if a stationary point is a local max/min or saddle point. (c) Know what it means geometrically for a set to be convex. (d) Know what it means geometrically for a function to be convex or concave. (Ignore Jensen’s Inequality) (e) Theorem 17.6 on page 628 is useful, but not necessary to know for the test. You do not need to know Theorem 17.7, either. (f) Know Theorem 17.8. It is particularly useful in combination with the theorems about determining concavity/convexity in sections 17.8 and 17.9. (g) Know Theorem 17.9. Notice 17.11 follows from Theorems 17.9 and 17.8. You should know 17.11, but it should be obvious if you know
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