The Extreme Value Theorem - Real Analysis | Lecture 13 скачать в хорошем качестве

The Extreme Value Theorem - Real Analysis | Lecture 13

In this lecture we state and prove the extreme value theorem. The statement of the theorem requires definitions of maximal and minimal values of a function, while the extreme value theorem itself states that any continuous function on a closed interval achieves maximal and minimal values. We further show that the range of a continuous function on a closed interval is itself a closed interval. Finally, we provide an illustrative example showing that a quadratic polynomial has a global minimum over the entire real numbers. This course is taught by Jason Bramburger.