MATH 20C Lecture 20

14.7 Optimization

How to classify critical points?

Answer: The second derivative test

Discriminant

of at
by

Theorem: The second derivative test for $f(x,y)$

Let be a critical point of . Assume are continuous near . Then

1. If and then is a local minimum.
2. If and then is a local maximum.
3. If , then is a saddle point.
4. If , the test is inconclusive.

Global Extrema

The minimum and maximum values of a function on a given domain are called global extreme values.

Bounded

A domain is bounded if it is contained in a disk of radius centered at the origin for some .

Closed

A domain is closed if it contains all boundary points.