Continuous Derivatives

This lecture covers the concept of continuous derivatives, including the conditions under which a function is continuously differentiable on an open interval, the properties of functions with continuous derivatives, and the analysis of extrema. The instructor explains the criteria for a function to be continuously differentiable, the relationship between the limit of the derivative and the function, and the behavior of functions at extrema points. The lecture also delves into the application of continuous derivatives in analyzing functions and determining critical points.