Differentiability: Continuous Strictly Monotone Functions

This lecture covers the concepts of continuous strictly monotone functions and their inverses, differentiability, the implication of differentiability on continuity, and provides various examples. The instructor explains the proofs and properties related to strictly monotone functions, injectivity, and the process of finding the best linear approximation for functions around a point. The lecture also delves into the general problem of approximating functions, starting with simple linear functions as an initial attempt. The importance of differentiability in approximating functions is highlighted through examples and the comparison between continuity and differentiability.