Lecture 15, Wednesday, 10/1/08: Section 12.7: Maxima/minima of functions of several variables

Topics

Local maxima/minima
Saddle points
First derivative test for functions of several variables. Critical points.
Second derivative test for functions of two variables.
Application: Least squares method (linear regression)

Read

Section 12.7 through Example 7.4 (inclusive). You can skip the remainder of the section (middle of page 1003 through end).

Homework

Section 12.7: 3, 5, 21, 27. Solutions.

Notes

While the first derivative test extends to functions of any number of variables, the second derivative test applies only to functions of two variables. In applied problems, the second derivative test is often unnecessary as it may be clear from the context whether the point found represents a maximum or a minimum, or neither.

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Last modified Sat 04 Oct 2008 04:11:46 PM CDT