Oxford Calculus - Classifying 2D Critical Points Using the Discriminant

Learn how to classify critical points for functions of two variables using the discriminant method in this 30-minute video tutorial by University of Oxford mathematician Dr. Tom Crawford. Explore the three types of critical points—maximum, minimum, and saddle point—with visualizations using the Maple Calculator app. Discover how to apply differentiation techniques from single-variable functions to multivariable functions for determining stationary points and nearby behavior. Follow along as Dr. Crawford derives the discriminant expression using Taylor Expansion for two-variable functions and explains its role in determining critical point types. Apply the classification system to a practical example, building on concepts from a previous tutorial on finding critical points. Access additional resources, including a Maple Learn worksheet and links to the Maple Calculator app, to enhance your understanding of this advanced calculus topic.

Introduction
Local maximum and minimum
Rate of change
Second order partial derivatives
Discriminant
Maximum and Minimum