General Instructions (repeated, but with alterations):

• While I will not rule out the occasional multiple choice question, generally speaking all questions will be free response requiring you to show all your work. The logical steps getting you to an answer are worth much more than the final answer itself
• Your objective on an exam is to demonstrate that you understand the concepts and can carry out essential calculations. Therefore, you should add enough detail to your answers to convince the grader that you understand what you are doing.
• Studying and practicing homework problems is important for and exam, but not all questions on an exam are drawn from the homework. Questions can also be based upon examples I or my TAs have covered in lectures and discussions.
• Theory is also important. You could be asked to state simple definitions, describe concepts, or even state and prove simple theorems. This is all part of learning what Calculus is all about.

Calculator Use Instructions:

• Calculators are permitted (TI 84 or lower) on exams.
• THE STORAGE OF NOTES OR FORMULAS IN YOUR CALCULATOR IS PROHIBITED!
• Exam proctors are allowed to examine your calculator at any time before, during, or after the exam. The presence of notes or formulas in your calculator will be treated as a violation of academic integrity (cheating)
• If you borrow a calculator from a friend, YOU are responsible for making sure that it does not contain stored notes and/or formulas

MidTerm Exam 3 Content:

Midterm Exam 3 will cover those sections of Chapter 3 outlined on the class syllabus

Chapter 3

Sec 1:

• be familiar with how to compute the linear approximation L(x) of a function at a point
• you should know the distinction between the increment in a function and the differential of a function and how one is used to approximate the other (see Eqn (1.5))
• be familiar with the type of calculation using approximations that appears in Example 1.3

Sec 2:

• know how to identify the basic undeterminate forms 0/0 and infinity/infinity when they arise in limits
• know the statement of L'Hopital's Rule and how to use it in basic cases
• be able to recognize the indeterminate forms other than the two basic ones and how to compute limits in these cases. In this regard, review Examples 2.6 through 2.11

Sec 3:

• there are a lot of definitions here with subtle differences, so be sure to be able to distinguish between them
• what does it mean to say that f(c) is an absolute maximum or an absolute minimum of f on a set S and remember how important the set is in this definition
• know the precise statement of the Extreme Value Theorem
• what does it mean to say that f(c) is a local maximum or a local minimum of f
• what does one mean by the critical numbers of a function, know how to find them in simple examples, and know why they are important (see Theorem 3.2)
• be familiar with Theorem 3.3 and Remark 3.3 and how this helps in finding absolute extrema such as in Example 3.11

Sec 4:

• what does it mean when we say that a function is increasing or decreasing on an interval I ?
• be able to determine, using the derivative of a function, the intervals on which the function is increasing and decreasing
• what is the "First Derivative Test" for local extrema, and can you apply it in simple cases?
• know how to handle examples with fractional exponents such as in Example 4.4

Sec 5:

• what does it mean when we say that a function is concave up or concave down on an interval I ?
• be able to determine, using the second derivative of a function, the intervals on which the function is concave up and concave down
• review Definition 5.2 and know how to find inflection points in simple cases
• what is the second derivative test for local extrema and how do you apply it?

Sec 6:

• don't worry about this section

Sec 7:

• be able to solve simple word problems involving optimization
  • review the steps involved at the top of page 308
  • then review Examples 7.1, 7.3, and 7.3 as examples of what to do

Sec 8:

• be able to solve simple word problems involving related rates
  • review the steps involved near the bottom of page 321
  • then review Examples 8.1, 8.2, 8.3 and 8.5 as examples of what to do

Sec 9:

• know what is meant by marginal cost and marginal profit for a problem in economics
• be able to determine marginal and actual cost in simple examples
• know what is meant by average cost for a problem in economics
• be able to determine minimum average cost in simple examples