Will s Guide To Life Volume 3 Math 220 Spring 2009 Preliminaries Remember that the work is more important than the final answer There is a limit on time so work hard and work efficiently do not spend all of your time working any one problem It is better to have studied too much and be overprepared than to understudy and do poorly You will be expected to know the definitions and statements of the major results and ideas covered in lecture You need to be able to state all hypotheses of the Theorems Do not waste time simplifying expressions unless specifically directed to do so or is required to answer the question Section 3 1 Linear Approximations and Newton s Methods The linear approximation of a function f at x0 Why this is sometimes called the Tangent line approximation Increments and differentials the picture that explains these Using linear approximations to approximate harder functions how to pick a good base point Newton s Method Where the formula for Newton s Method comes from Section 3 2 Indeterminate Forms and L Ho pital s Rule The Indeterminate forms that work for L Ho pital s Rule What needs to be true in order to use L Ho pital Manipulating other indeterminate forms into forms on which L Ho pital can be used Why indeterminate forms are indeterminate Section 3 3 Maximum and Minimum Values Definitions of absolute and local extrema The difference between absolute and local extrema The Extreme Value Theo 1 rem critical numbers and Fermat s Theorem The relationship between critical numbers and extrema Section 3 4 Increasing and Decreasing Functions Definition of strictly increasing and decreasing functions relation to the derivative Why this relationship is true MVT The First Derivative Test Section 3 5 Concavity and the Second Derivative Test Concave up and concave down what this means for the function and its derivatives Inflection points The Second Derivative Test Section 3 6 Overview of Curve Sketching Using the results of sections 3 3 3 5 and previous chapters to aid in accurately sketching graphs of functions The important things you need to check to do this Section 3 7 Optimization How to turn a word problem into a calculus problem then do the appropriate calculus to solve the problem and finally give a physical solution to the word problem Optimizing functions given constraints This will require some use of geometry and other math skills Applications in real life where optimization is necessary Section 3 8 Related Rates Setting up word problems into calculus Related rates as an application of implicit differentiation Other Info The exam will test both your knowledge of the concepts and ideas presented as well as your ability to work problems Remember that the right work is far more important than the right final answer 2 Be sure to clearly indicate your final answer to a problem by boxing or circling and labeling it as your final answer The best way to study is to re read your lecture notes and the book work through the suggested homework problems and look over your graded work Learn from the mistakes you have made on quizzes and homework do not repeat them on the exam For more Math 220 related information be sure to check the course website www math uiuc edu wgreen4 math220 spring09 html 3