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 fx(x,y) and fy(x,y). Look at problems 15.3.17-22.
- Find fxx, fyy, fxy, and fyx. 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