Differentiability and Hessians

This lecture covers the concept of functions of class C^p, the Hessian matrix, and methods to verify the differentiability of a function at a point. It explains the conditions for a function to be of class C^p, the symmetry of the Hessian matrix, and practical examples. The instructor demonstrates two methods to check the differentiability of a function at a given point, emphasizing the importance of continuity of partial derivatives. Through examples and theoretical explanations, students learn how to apply these concepts in mathematical analysis.