Math 130-03, Spring 2001 Information for the Third Test ----------------------------------------------------------------------------- The last in-class test in this course takes place in class on Friday, April 20. It covers Chapter 4, Sections 1,2, 4, and 5; Chapter 5, Section 1; and Labs first three labs 9, 10, and 11. Of course, you are also responsible for previous material, especially the derivative formulas that were covered on the previous test. Here are some of the terms and ideas that you should have mastered for this test: All the derivative formulas that you learned previously Inverse functions Inverse functions as "undo" operations Domain and range of an inverse function Finding an inverse function from a formula Finding an inverse function from a graph One-to-one function Horizontal line test Restricting the domain of a function to get an invertible function The derivative of an inverse function Exponential functions The number e Logarithmic functions Logarithmic functions are the inverse functions of exponential functions The natural logarithm, ln(x) Properties of exponential functions Properties of logarithmic functions Using inverse functions to solve equations Solving equations involving logs and exponentials Derivative formulas for logarithmic and exponential functions Using the chain rule with logarithmic and exponential functions Inverse trigonometric functions: arcsin, arccos, arctan, arcsec Derivatives of the inverse trigonometric functions Related rates Solving related rate word problems (This is a big one!) A function that is increasing or decreasing on an interval Relationship of the first derivative to increasing/decreasing A function that is concave up or concave down on an interval Relationship of the second derivative to concavity Relationship of the first derivative to concavity Inflection point Drawing graphs of functions, using derivatives, concavity, etc. Reading properties such as increasing/decreasing or concavity from a graph