Exam 1 Study Guide



Study Guide for Exam 3

General Information

• Exam 3 will be held in class Wednesday, April 29. Exams will be passed out at 1:30 p.m., and all exams will be collected at 2:35 p.m. If you choose to arrive late or leave early, please be considerate of your classmates.

• The exam will cover Sections 10.2-10.5, 11.1 of your textbook and the two handouts on sine and cosine functions. Facility with Chapter 1 and Sec 2.1-2.2, sec 9.3-9.8, 10.1 is assumed.

• The exam is closed-book. You may write directly on the exam (no blue books). A calculator may prove helpful. Cell phones and other devises that transmit will not be allowed and must be stowed.

• Always show your work. Partial credit may be awarded provided the reasoning is solid and work is shown in a clear and organized fashion. A few points on the test will be reserved specifically for the clarity and neatness of your solutions.

• The exam will emphasize concepts and understanding over brute force computation.

Things you will be expected to a) be able to do and b) explain on the exam

1. Find and identify inflection points of a function.

2. Understand and use the connections between the first and second derivatives of a function and whether the function is increasing/ decreasing and concave up/down. You may need to sketch a graph given info about the first and second derivative, or use equations to determine information about the concavity, etc.

3. Find the locations (x-values) and values (y-values) of relavitve extrema of a function. Use the second derivative test to determine what time of relative extrema it is.

4. Combine #1 – #3 with asymptotes, intercepts, etc. to generate graphs of functions.

5. Find the locations (x-values) and values (y-values) of absolute extrema of a function. Interpret the absolute extrema to explain what is happening in a given situation (i.e. what does it tell you about sales, profit, growth, etc)

6. Set up and solve an optimization problem. You would need to set up an objective function and perhaps a constraint equation. Equations for the area and circumference/perimeter or squares, circles, and triangles is assumed, as is the volume of a rectangular solid, the area of its sides, and how to put together a cost, revenue and/or profit function.

7. Evaluate sine and cosine using a calculator (make sure it’s set to radians)

8. Take derivatives of functions involving sine and cosine.

9. Determine if a function is a solution to a differential equation; given a general solution to a general differential equation, construct the solution for a specific differential equation.

Preparing for the Exam: Since the exam will emphasize the understanding of concepts, it may be useful to prepare using the following methods (assuming you’ve already done all your homework, gone back through it, and figured out what you didn’t understand at the time). Outline the major concepts. Then, write out directions or a list of steps you would follow to solve each of the problem types listed above. Finally, make up one to three problems of each type, and make sure you can solve and explain them! Trade problems with a partner and solve their problems too (it’s usually more fun to study with someone and, if done well, forces you to be able to explain what you mean).

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