# Math 190: Study Guide - Chapter 8

1. A function of several variables is given, evaluate it at three points. Look at problems 8.1.1-10.
2. Find the first partial derivatives of the function. Two parts. Look at problems 8.2.1-22
3. Find the second-order partial derivatives of the function. Two parts. Look at problems 8.2.33-40.
4. Find the critical points of the function. Then use the second derivative test to classify the nature of each point, if possible. Finally, determine the relative extrema of the function. Two parts. Look at problems 8.3.1-20.
5. Use the method of Lagrange multipliers to optimize the function subject to the given constraint. Look at problems 8.5.1-16.
6. Evaluate the double integral. Two parts. These integrals are already set up, so there isn't really anything like it in the textbook to look at.
7. Evaluate the double integral over the region. Sketch the region R before integrating. Look at problems 8.6.1-25.
8. Find the volume of the solid bounded above by the surface z=f(x,y) and below by the plane region R. Sketch the region R before integrating. Look at problems 8.6.34-41.

## Notes

• Many of the problems on the test are taken directly from the textbook.
• Since there are few problems, each problem is worth a lot of points.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 Total 12 12 16 18 10 12 10 10 100