In this lesson, you will see examples of functions which are strictly increasing, yet their derivative is not positive. Then you will learn precisely what it means for an interval to be increasing, strictly increasing, decreasing, or strictly decreasing. Then you'll learn how the sign of the derivative can imply a function is increasing, decreasing, etc. You'll then see a proof for each of these implications. Before attempting to understand the proofs, you must know the mean value theorem.