Intermediate Value Theorem

This lecture covers the Intermediate Value Theorem, which states that a continuous function on a closed bounded interval reaches its supremum, infimum, and every value in between. It also discusses the corollaries related to finding solutions of equations and the properties of continuous functions. The lecture further explores the geometric interpretation of functions, the concept of derivatives, and the proposition that a function differentiable at a point is also continuous at that point. Additionally, it delves into the notion of infinite derivatives and the implications for the graph of a function. The lecture concludes with examples illustrating the application of these theorems and concepts.