# Lecture 10: Second derivative test; and boundaries and infinity

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Taught by OCW
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Lesson Summary:

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.

Lesson Description:

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.

Additional Resources:
Questions answered by this video:
• How can you determine if a critical point is a local minimum, a local maximum, or a saddle point?
• How do you find global minimum and maximum points of a function?
• What is the second derivative test?
• How can you tell what a critical point is using 4ac - b^2?
• What is the quadratic approximation formula?
• What are the critical points of f(x,y) = x + y - 1/xy?
• #### Staff Review

• Currently 4.0/5 Stars.
This lesson continues the idea of critical points and minimum and maximum optimization problems to find global maxima and minima. This proves to be much more interesting and fulfilling than the previous lecture, as you can determine much more about the graph using the second derivative test. At the end of the lecture, an actual concrete problem is done.