About the final exam
For the final exam you may prepare 2 pages of notes (both sides).
You may use any calculator (but not a phone nor an iPad).
Content
You are responsible for all the topics from the whole course, including notes on the class website, all the labs, and textbook sections. However Chapter 1 will be de-emphasized. See the class website for the sections we covered.
You should be able to:
- Interrelate and use symbolic, graphical, numeric, and verbal representations of functions, differentiation, antidifferentiation, and integration, to solve pure and applied problems.
See the review pages for
Preparation
Use your textbook: I recommend that you solve some or all of the Review Problems and Check Your Understanding exercises at the end of the chapters
Functions
- Use four ways of representing a function: verbal description, table (numerical data), graph, formula.
- Recognize linear and exponential functions from a table and write formulas for them.
Review Problem: p 80, #41
Rates of change and derivative functions
- Interpret the derivative as a rate of change
- Use a local linear approximation to estimate values of a function near a given point
- By looking at the graph of a function determine the points where the first and second derivatives are positive/negative/zero.
- Using the graph of a function, estimate the derivative at a point
- Compute derivatives symbolically, using the product, quotient, and chain rules
Review Problems: p 121 (and following) #5, 14, 20, 25, 28, 35
Net change, integrals, and antiderivative functions
Review Problems: p 264 #2, 20, 25, 26; p 322 #13, 19, 21, 24, 32, 34; p 312 #22-25
Applications of the derivative and partial derivatives
- Locate critical points, local max/min points, inflection points from the graph of the derivative
- Compute first and second order partial derivatives
- Find local max/min points for functions of two variables using the second derivative test
- From a contour diagram, determine the signs of partial derivatives, locate critical points, local and global max/mins
Review Problems: p 223 #13; p 389 #1; p 380 #5, 6, 11
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