Unit 8 - Sections 4.2 to 4.4

Module Overview

There is some vital stuff in this unit.  Section 4.3, on graphing functions, ties together every single topic we have looked at so far, other than word problems.  A good graphing question involves arithmetic, limits, first and second derivatives, and combinations of these, together with the actual graphing.  Section 4.4 deals with optimization and gives us the word problems that are not there in the previous section.  Between these two, we cover everything that we have done before in this class.  Make sure that you understand this material as well as possible and ask as many questions as you can.

Learning Outcomes

• Section 4.2: We finish up Section 4.2 by looking at the second derivative and its effect on a function. We learn the Second Derivative Test and why it is nearly useless in first-year Calculus, but becomes very important next year.
• Section 4.3: One of the most important sections in the book, the subject of graphing uses every method we have developed so far. Other than word problems, we need to bring together all of the other knowledge gained in this course to do the questions here.
• Section 4.4: Having worked through the intense calculations of the graphing section, we immediately return to word problems. With the idea of max and min now available, we can try to optimize various physical values. Translating a word problem into mathematics and understanding the constraints involved (we are, after all, usually optimizing over an interval) is a skill that requires a lot of practice.