The Mystery Of Solved
Most calculus books give the formula in the title and some conditions for determining whether a critical point of a real-valued function of two variables is a maxima, minima, saddle, or unknown. There is usually no explanation of why the formula works nor is there given any method for determining maxima or minima for real-valued functions of more than two variables. In this talk, we will show how a little bit of linear algebra and our experience from one dimensional calculus can fill both of these holes. For courses that do not have linear algebra as a prerequisite, the material presented can be adapted into a project.