About This Course
In this course, you will learn how to analyze and optimize multivariable functions using partial derivatives and Taylor expansions. You will start by visualizing three-dimensional surfaces and computing first, second, and mixed partial derivatives. Then, you will use these tools to build local polynomial approximations, classify critical points, and find absolute extrema on closed regions. Finally, you will apply these mathematical techniques to tackle real-world constrained optimization problems across geometry, business, and biology.
What You'll Learn
- Compute first, second, and mixed partial derivatives to analyze the slope and curvature of three-dimensional surfaces.
- Construct two-variable Taylor and Maclaurin expansions to approximate complex functions with local polynomials.
- Identify and classify critical points as relative minima, maxima, or saddle points using the Second Partials Test.