In this lesson, you will learn about critical points and how to determine if they are a minimum, maximum, or saddle point using the second derivative test. The lesson provides an example of a quadratic function to illustrate how to complete the square to determine if the critical point is a minimum or maximum. It also emphasizes the importance of checking the boundary and infinity behavior of the function to locate the global minimum or maximum. Overall, the lesson provides a useful tool for analyzing critical points in functions of two variables.
Learn about the second derivative test and how it can be used to determine things about critical points.
Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 15, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.