Contour Plots and Critical Points

Lang Moore and David Smith, Duke University

with the assistance of
Jer-Chin Chuang, Furman University
John Michel, Marietta College

Purpose: To use contour plots and second-degree Taylor approximations to locate extreme points and saddle points of a function of two variables.

Prerequisites: Familiarity with

• partial derivatives,
• critical points,
• the second derivative test,
• contour plots,
• Taylor approximations for a function of two variables.