Taylor Expansion and Convex Functions

This lecture covers the concepts of Taylor expansion and convex functions. It starts by discussing the convexity of the sum of two convex functions. Then, it delves into Taylor expansions of functions and their properties, such as differentiability. The lecture also explores the conditions for a function to admit a Taylor expansion of a certain order. Additionally, it explains the notion of Lipschitz continuity and its implications for functions. The examples provided illustrate the application of these concepts in various scenarios.