Mathematics 135 -- Calculus 1
Exam 3 -- Things to Know
November 20, 2019
General Information
The third full-period exam of the semester will be given
in class on Friday December 6. It will cover the
material from sections 4 - 9 of Chapter 3 and sections 2 - 7 of Chapter 4.
(basically since the last exam, or Problem Sets 6,7 and 8, plus
the material from Friday, November 22 amd ). There will be eight or nine questions
(maybe grouped together as parts of larger questions) similar to problems from the problem sets,
and in-class practice problems.
As before, graphing calculators will be allowed on this exam..
Material To Know
You should know the following material.
- As you will have realized, almost all of the stuff from Chapters 1, 2 and the start
of Chapter 3, especially things about operations on functions,
various classes of functions, all of our techniques for computing limits, continuity,
the definition of the derivative of a function, derivative rules for powers, exponentials,
the product and chain rules, etc. is relevant here too. The new material is:
- Section 3.4: There will not be as much emphasis on this section as the others,
but you should recognize that if a question asks for an instantaneous rate of
change of some quantity, then mathematically, it is asking for the derivative
of that quantity with respect to whatever variable is specified.
- Section 3.5: Higher derivatives. Be able to compute any of these. (The rules
are exactly the same as in 3.1, 3.3, etc. because, for instance, f '' = (f')'.)
- Section 3.6: Derivatives of trigonometric functions. Know the derivative
rules in Theorems 1 and 2 from this section, and be able to apply them in combination
with the other rules from 3.1, 3.2, 3.3, etc.
- Section 3.7: The Chain Rule (for derivatives of compositions) -- Know what it
says and how to apply it in combination with the other rules from 3.1, 3.2, 3.3, 3.6.
- Section 3.8: Implicit differentiation
- Section 3.9: Derivatives of ln(x), sin-1(x), tan-1(x)
separately and in combination with the other derivative rules
- Sections 3.10 and 4.1: We did not discuss these; you are not responsible for that material.
- Section 4.2: Extreme values. Know how to find the maximum and minimum values
of a continuous function on a closed interval.
- Section 4.3: The Mean Value Theorem and consequences including the First Derivative Test.
- Section 4.4: Second derivatives and concavity, the Second Derivative Test.
- Section 4.5: L'Hopital's Rule: Know how to apply this compute indeterminate limits
of the
0/0, ∞/∞, 0 ⋅ ∞, and 1∞ forms
- Section 4.6: This section is mostly about using the ideas from 4.2 - 4.4 to sketch
graphs by hand. I might ask you to do some of this, or I might give you the formulas
for f '(x) and/or f ''(x) to minimize the consequences of a small mistake
in computing those if you had to deal with a complicated function with vertical or horizontal
asymptotes, etc.
- Section 4.7: Applied optimization problems. Be prepared for one like the problems
from the worksheet for November 22 and 25.
Good Review Problems:
Try a good selection of the review problems from Chapter 3 and Chapter 4 in the book.
If the functions used are unfamiliar (i.e. ones we have not discussed), you're not
responsible for them.
Also see the sample exam questions posted on the course homepage.