Iain and Jean’s Midterm 2 Study Notes December 11, 2005 Things to Know I. The Basics a. Trig identities, properties of logarithms b. Derivatives i. Logarithmic differentiation ii. Implicit differentiation c. Graphs i. Asymptotes/continuity ii. increasing/decreasing iii. concavity iv. relative extrema II. Mean Value Theorem a. Related: Extreme Value Theorem, Fermat’s Theorem III. L’Hospital’s Rule a. Interdeterminate vs. determinate forms IV. Applications a. Linearization – equations of tangent lines b. Related rates i. Strategies 1. Draw a diagram. 2. Figure out what is changing with respect to what else 3. Find a way to relate the variables 4. Differentiate and solve c. Optimization i. Draw a diagram ii. Figure out what you are optimizing and what you are changing iii. Find a way to relate the variables iv. Differentiate and solve Wrap-up: What to Expect (Breakdown of types of problems to know) • Differentiation (a few problems) – make sure you know how to use and apply all rules, know when to use logarithmic differentiation (even though they’ll probably tell you) • Implicit Differentiation – be able to use it flexibly, don’t be scared of graphs • Graphs (increasing/decreasing, concavity, etc.) • Mean Value Theorem – know it well! (very underrated) • L’Hospital (a few problems) • Related rates • Optimization Tips for Studying • Make yourself a study sheet that includes formulas, statements of important theorems, and examples of special graphs, etc. • Don’t psych yourself out if you see something unfamiliar on the test—with a little finagling, you will be able to change it into a familiar form • Don’t be overwhelmed by the number of practice problems you think you have to do—it is far more important to understand concepts. It is much more important to understand concepts than to memorize ways to do problems. • If you do want good practice problems, old worksheets are a good place to look. • Get a good night’s sleep. • Eat lots of candy, or find some other way to
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