Intermediate Value Theorem

This lecture covers the Intermediate Value Theorem, which states that for a continuous function on a closed interval, every value between the function's maximum and minimum is attained. The theorem is illustrated through examples of continuous functions and the verification of their continuity. The lecture also discusses the projection function, the concept of continuity in two dimensions, and the verification of functions' continuity. The instructor explains the theorem's application in proving the existence of roots of functions and emphasizes the importance of continuity in mathematical analysis.