## Math 221 - Chapter 15 Study Guide

- Sketch the domain of the function f. Look at problems 15.1.15-18.
- Sketch the level surface. Look at problems 15.1.37-40.
- Find the limit, if the limit exists. Two parts. Look at problems 15.2.25-32.
- Find f
_{x}(x,y) and f_{y}(x,y). Look at problems 15.3.17-22.
- Find f
_{xx}, f_{yy}, f_{xy}, and f_{yx}. Look at problems 15.3.43.
- Find dz/dt using the chain rule. Look at problems 15.4.1-6.
- Related rate application problem. Look at problems 15.4.25-29.
- Find equations for the tangent plane and normal line to the given surface at the point P.
Look at problems 15.5.1-8.
- Find the gradient of
*f* at the indicated point. Look at problems 15.6.7-10.
- Find the directional derivative of
*f* at P in the direction of *a*. Look at problems 15.6.15-20.
- 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 15.6.29-36.
- Find the differential dw. Look at problems 15.7.39-42.
- Use a tree diagram to construct the formulas for the chain rule. Look at figures 15.7.7-10.
- Find all relative maxima, relative minima, and saddle points. Look at problems 15.8.9-20.
- 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 15.9.3-10.

### Notes:

# |
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 |