Concavity and Convexity: Analysis of Functions

This lecture covers the concepts of concavity and convexity in functions, including the definition of local maximum and minimum points, the criteria for concavity and convexity, and the analysis of piecewise defined functions. The instructor explains how to determine concavity and convexity using the first and second derivatives of a function, and provides examples to illustrate these concepts. Additionally, the lecture discusses the properties of concave and convex functions, the identification of critical points, and the analysis of singularities in functions.