Dave's Web Corner

MTH-261 Week 7 (October 6-12)

recommended exercises
- 3, 7, 11, 17, 21, 27, 31, 34, 35, 42, 45, 49, 54
learning objectives
- use partial derivatives to locate critical points for a function of two variables
- apply the second derivative test to identify a critical point as a local maximum, local minimum, or saddle point for a function of two variables
- examine critical points and boundary points to find absolute maximum and minimum values for a function of two variables
additional notes
- checking the boundary of a region, where present, for extreme values is absolutely necessary.
- the analyses of the boundary of a region and the interior of a region are separate processes
- the second derivative test can only be used in the interior of a region

recommended exercises
- 5, 9, 14, 17, 25, 31, 37, 43, 48
learning objectives
- use the method of Lagrange multipliers to solve optimization problems with one constraint
- use the method of Lagrange multipliers to solve optimization problems with two constraints
additional notes
- maximize/minimize with one constraint
  - the gradients are colinear at the locations of extreme values
    - the gradient of the objective function is a multiple of the gradient of the constraint function
- maximize/minimize with two constraints
  - the gradients are coplanar at the locations of extreme values
    - the gradient of the objective function is a linear combination of the gradients of the constraint functions
- solving nonlinear equations
  - following the branches of a tree

Deadlines
- All homework is due at the beginning of class on the date indicated.
- All exams are given in class on the date indicated.
- Late homework is not accepted and there are no make-ups for missed exams. Contact me before the deadline if you have a conflict with a deadline and we will find a mutually agreeable solution.
- Solutions are posted under these links after the deadline.
Homework
- due Thursday, October 10:
  - 24, 25, 26
- due Thursday, October 17:
  - 14.6 - , 14.7 - , 14.8 -
- due Thursday, October 24:
  - 15.1 - , 15.2 - , 15.3 -
Exams
- Thursday, November 7: Exam 2
  - Exam 2 (solutions)
  - Exam 2 covers sections 14.4-14.8 and 15.1-15.7