The Extreme Value Theorem

The extreme value theorem sits alongside the intermediate value theorem.

They are both very intuitive and very important theorems about real valued functions which are continuous over a closed interval [a,b].

The extreme value theorem is that such a function must be bounded and must obtain its minimum and maximum.

In this video we firstly explain this theorem further and see why it makes intuitive sense and then we prove it from the abstract analytical definition of continuity.