Mathematics 135 -- Calculus 1

Exam 3 -- Things to Know

November 18, 2016

General Information

The third full-period exam of the semester will be given in class on Friday December 2. It will cover the material from sections 3 - 10 of Chapter 3 and sections 2 - 4 of Chapter 4. (basically since the last exam, or Problem Sets 6,7 and 8, through the material from Friday, November 18). There will be eight or nine questions (maybe grouped together as parts of larger questions) similar to problems from the quizzes, problem sets, and in-class practice problems so far. Graphing calculators will not be allowed on this exam..

I will be happy to run an evening review session for the exam the week after we return from Thanksgiving break.

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 piecewise-defined functions, operations on fuctions, various classes of functions, all of our techniques for computing limits, continuity, the definition of the derivative of a function, etc. is relevant here too. The new material is:
• Section 3.3: The Product and Quotient Rules for derivatives. Know the statements of both well and be able to use them separately and in combinations.
• 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
• Section 3.10: Related rates problems. You should be prepared for a question similar to the ones from the group discussion from November 9 and 11.
• Section 4.1: We did not discuss this; 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.

Good Review Problems:

There is an optional WebAssign Exam 3 review assignment posted. You could also try a good selection of the odd-numbered problems 17 - 107, 115, 117, 119 from the Chapter 3 review and 31, 33, 35, 37, 41, 43, 47, 49, 57 from the Chapter 4 review.

Also see the sample exam questions posted on the course homepage.