Lecture 9: Max-min problems and least squares.
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Lesson Description:
A lecture on finding maximum and minimum points as well as the least squares analysis.
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:
- Problem Set - A problem set with some problems from this lecture.
- Lecture Notes - Lecture Notes from this lesson.
- Transcript of Lesson - Written transcript from this lesson.
Questions answered by this video:
- What is the approximation formula for delta z with respect to delta x and delta y?
- What is the tangent plane approximation?
- What is the equation of a plane?
- How do you solve optimization problems using partial derivatives?
- How can you find the minimum and maximum values for a function with two variables?
- Why is the tangent plane to a function horizontal?
- What is a critical point of a function of two variables?
- How can you determine if a critical point is a local minimum, a local maximum, or a saddle point?
- What is a least-squares interpolation?
- How can you find the best fit line for a set of data?
- What is the formula for the least squares regression line?
- How can you find the best quadratic function fit for a data set?
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Staff Review
This lesson tangent plane approximations, optimization problems using partial derivatives, critical point analysis, and the least squares interpolation method. These are all very important topics, explained very well in the lecture. This is a really interesting and important lecture in this course.
