Local Maximum and Minimum Values/ Function of Two Variables

Finding Local Maximum and Minimum Values of Functions with Two Variables
In this video, you’ll explore how to find local maximum and minimum values for functions of two variables using derivatives. We outline the general procedure and walk through a complete example, demonstrating how to use second partial derivatives to identify critical points. This is a crucial technique for students diving deeper into multivariable calculus and wanting to master optimization problems!

What You Will Learn
How to apply second partial derivatives to find local extrema of functions of two variables.
How to calculate the discriminant D(a,b) to classify critical points as maxima, minima, or saddle points.
An example problem illustrating the step-by-step process of identifying and classifying local extrema.
Understanding how to find maximum and minimum values in functions of two variables builds on concepts from single-variable calculus. In this tutorial, we extend the ideas of using first and second derivatives to a multivariable context, where you’ll learn how to calculate second partial derivatives and apply the discriminant formula D(a,b)=f_xx(a,b)* f_ yy(a,b)−[f_ xy(a,b)] ^2 to classify critical points. This example will help clarify how to work through these computations and apply them to real-world problems.

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