### 4 videos in "Partial Derivatives, 2nd Derivatives, Rules, and Least Squares"

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

Lecture 10: Second derivative test; and boundaries and infinity

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Part of video series Calculus 3 Course acquired through MIT OpenCourseWare

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.

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Learn about the second derivative test and how it can be used to determine things about critical points.

- Transcript of Lesson - Written transcript from this lesson.
- Lecture Notes - Lecture Notes from this lesson.
- Problem Set - A problem set with some problems from this lecture.

- 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?

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.