Math 221 - Chapter 16 Study Guide

1. Sketch the domain of the function f. Look at problems 16.1.14-19*.
2. Sketch the level surface. Look at problems 16.1.48-51*.
3. Find the limit, if the limit exists. Two parts. Look at problems 16.2.13-35*.
4. Find f_x(x,y) and f_y(x,y). Look at problems 16.3.7-12*.
5. Find f_xx, f_yy, f_xy, and f_yx. Look at problems 16.3.21-26*.
6. Find dz/dt using the chain rule. Look at problems 16.4.19-24*.
7. Related rate application problem. Look at problems 16.4.44-48*.
8. Find equations for the tangent plane and normal line to the given surface at the point P. Look at problems 16.5.1-8*.
9. Find the gradient of f at the indicated point. Look at problems 16.6.5-8*.
10. Find the directional derivative of f at P in the direction of a. Look at problems 16.6.13-18*.
11. Find a unit vector in the direction in which f most increases or decreases most rapidly at P; and find the rate of change of f at P in that direction. Look at problems 16.6.27-34*.
12. Find the differential dw. Look at problems 16.7.33-36*.
13. Use a tree diagram to construct the formulas for the chain rule. Look at figures 16.8.1-16.8.5.
14. Find all relative maxima, relative minima, and saddle points. Look at problems 16.9.1-20*.
15. Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint. Also, find the points at which these extreme values occur. Look at problems 16.10.1-7*.

Notes:

• *'d problems are directly from the text.