Global and local extrema of functions

This lecture covers the concepts of global and local extrema of functions, defining them based on the values of the function at specific points. It explains how a function can have a global maximum at a point where its value is greater than or equal to all other points in the domain, and a local maximum at a point where its value is greater than nearby points. The lecture also discusses the possibility of functions having no maximum or minimum values, illustrating this with examples. Additionally, it introduces the theorem that guarantees the existence of global maximum and minimum values for continuous functions over a closed interval.