# Lecture 9: Max-min problems and least squares.

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Lesson Summary:

In Lecture 9, viewers will learn how to apply partial derivatives to handle minimization or maximization problems involving functions of several variables. The lecture covers the approximation formula for changes in the value of f when both x and y are changed, and how to use this formula to estimate how the value of f changes in max-min problems. The lecture also introduces critical points, which are points where partial derivatives are zero, and explores the three possibilities for critical points: local maxima, local minima, or saddle points.

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.

• 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?
• #### Staff Review

• Currently 4.0/5 Stars.
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.