Extreme Values Theorem

This lecture covers the Extreme Values Theorem, which states that for a continuous function f defined on a closed interval [a, b], there exist points c in [a, b] such that f(c) is the maximum and minimum value of f on [a, b]. The lecture also includes the proof of this theorem and discusses the concept of image set of a function. Additionally, it explores the implications of the theorem on the behavior of continuous functions within an interval, emphasizing the existence of extreme values and the continuity of the function.