The Mystery Of Solved

Jeffrey A. Graham, Susquehanna University

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.