Nature of Extremum Points

This lecture discusses the nature of extremum points in the context of functions of class e². Starting with the simplification of equations around the point (0,0), the instructor explores the eigenvalues and Hessians to determine the behavior of functions in the vicinity of extremum points. The lecture delves into the concept of orthogonality and the implications for extremum points, emphasizing the importance of understanding the behavior of functions in the neighborhood of critical points. Various cases are analyzed to determine the nature of extremum points and the conditions under which they occur.