## Math 221 - Chapter 16 Study Guide

- Sketch the domain of the function f. Look at problems 16.1.14-19*.
- Sketch the level surface. Look at problems 16.1.48-51*.
- Find the limit, if the limit exists. Two parts. Look at problems 16.2.13-35*.
- Find f
_{x}(x,y) and f_{y}(x,y). Look at problems 16.3.7-12*.
- Find f
_{xx}, f_{yy}, f_{xy}, and f_{yx}. Look at problems 16.3.21-26*.
- Find dz/dt using the chain rule. Look at problems 16.4.19-24*.
- Related rate application problem. Look at problems 16.4.44-48*.
- Find equations for the tangent plane and normal line to the given surface at the point P. Look
at problems 16.5.1-8*.
- Find the gradient of
*f* at the indicated point. Look at problems 16.6.5-8*.
- Find the directional derivative of
*f* at P in the direction of *a*. Look at problems 16.6.13-18*.
- 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*.
- Find the differential dw. Look at problems 16.7.33-36*.
- Use a tree diagram to construct the formulas for the chain rule. Look at figures 16.8.1-16.8.5.
- Find all relative maxima, relative minima, and saddle points. Look at problems 16.9.1-20*.
- 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.

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
Total |

Pts |
4 |
4 |
8 |
6 |
12 |
6 |
8 |
6 |
6 |
6 |
6 |
6 |
6 |
8 |
8 |
100 |