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.
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.