The Derivative
At the end of Part 2, you learned the basics of the difference quotient and that it calculates something called the derivative. In the study of calculus, the derivative is huge. Just about everything you do from here on out is going to use derivatives to some degree. Therefore, it’s important to know exactly what they are, when they do and don’t exist, and how to find derivatives of functions.
Once you’ve got the basic skills down, you can begin to explore the huge forest of applications that comes along with the derivative package. Since derivatives are actually rates of change, they classify and describe functions in ways you’ll hardly believe. Have you ever wondered, “What’s the maximum area I could enclose with a rectangular fence if one side of the rectangle is three times more than twice the other side?” If you have, well, you scare me because no one has thoughts like that. However, the good news is that you’ll be able to find your answer once and for all.