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:

  1. 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

  • Estimate net change from a graph of the rate of change
  • Estimate the net change from a table of the rate of change
  • Evaluate indefinite integrals using antiderivative formulas and the technique of substitution
  • Evaluate definite integrals using the fundamental theorem of calculus

    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