# Math 221: Chapter 14 Study Guide

- Find the limit, if the limit exists. Three parts.
- Find f
_{x}(x,y) and f_{y}(x,y).
- Find the differential.
- 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.
- Find the directional derivative of f at P in the direction
of
**a**.
- Locate all relative maxima, relative minima, and saddle values, if any.
- Find equations for the tangent plane and normal line
to the given surface at the point P.
- Use a total differential to approximate the change in the values of a function from point P to point Q.
- Use the chain rule to find the partial derivatives and the derivative.
Three parts.
- Find the gradient of f at the indicated point. Find unit vectors in the directions in which f
increases and decreases most rapidly at P; and find the rate of change
of f at P in those directions.
- Find parametric equations of the tangent line at the given point to the curve of intersection of two surfaces.
- Find some second order partial derivatives. Three parts.
- Identify the three dimensional surface (see chapter 12). Six parts.
- Find the scalar tangential and normal components of acceleration at the given time.
- Find an arc length parametrization of the function that has the same orientation and the indicated reference point.

## Notes

- Some of the problems may be directly from the text.
- The questions are worth a lot of points each since there aren't very many of them.

## Points per problem

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

Pts |
15 |
10 |
5 |
10 |
8 |
10 |
10 |
7 |
15 |
10 |
10 |
12 |
12 |
8 |
8 |
150 |