Exam 2 Review Sheet
The Standard Caveat:
Any review sheet is a compilation of personal opinions about
the relative importance of various parts of the material. These are jason's. It would be
crazy to rely on any single resource to study for your Exam, including this little study
guide! This time, to make my point, I intentionally left off only 2 key concepts. What
are they?
This exam will cover:
•
3.1-3.7, and 3.9
•
4.1-4.5
Yes, indeed, we really did skip.
..
•
3.8 and 3.10
Chapter 3
Of course, Chapter 3 contains all the material necessary to pass the
gateway exam. It is tempting to imagine that once the gateway has been mastered, so
has Chapter 3. If you convince yourself of this, you'll be in for a rude surprise: We
have already tested you on rote differentiation skills, and we don't plan to do it again.
It is unlikely that you'll find questions which ask you simply to differentiate formulas.
Expect story problems, interpretive problems, and various other complexities. Look
over your group homework to find the kinds of complex word problems we expect
you to solve.
3.1
I can differentiate polynomials, can you? I admit, this is mostly gateway material.
Constant multiple, sum, and power rules allow us to differentiate many functions, and
leave many still impossible. It's all pretty basic looking back. One warning: As you
learned on the gateway, a constant is a constant is a constant. Even if it looks like
ln(Pi)*sin(3e+4), it's just a constant. Treat it appropriately!
3.2
The only thing here which isn't essentially gateway training is the nice observation
that the derivative of a
x
is proportional to the value of a
x
(even as x changes). We
could now deduce this fact from the fact that d/dx (a
x
) = ln(a) a
x
, which even tells us
the constant of proportionality. Despite my claim that this is "gateway training," it is
still possible to write a story problem. See 3.2.36 for a typical one. Notice that this is
just a "differentiate this function" problem inside a very thin plastic wrapper marked
"Section 2.5". In other words, there are no new deep and difficult conceptual notions
here.
3.3
Let me continue the warnings now. The product rule is not just about gateway
skills, as you can see by looking over the problems in 3.3. Problems 3.3.40-3.3.44 are
all new conceptual problems, testing not just your ability to differentiate and interpret,
but also your ability to understand the inner workings of the product rule. Sometimes