Courses   <-  Sean Forman   <-  You Are Here Applied Calculus I

April 19, 2005

Second Exam Review. The second exam is Thursday, April 21, 2005.

You will need a calculator capable of doing trig functions, though many problems will ask you to do them using the unit circle. Any calculator capable of doing symbolic differentiation will not be allowed (for example the TI-89 and above). You will not have any notes or formulas available to you. Here is a summary of topics covered in the first part of the course. There may be other topics not listed here. You are responsible for all material covered in class and on homework.

The solutions to all assigned homework problems is available on reserve in the library. Go to the front desk and ask for the homework solutions to Dr. Forman's Math 1251 class. The exam will be designed so that you should be able to complete it in 75 minutes.

1. Section 3.1 Graphing using the first derivative. Finding critical values. Intervals where the function is increasing or decreasing. First derivative test. Sketching given the sign diagrams. I could ask a question such as: if $f'(x) = x-2$, which of the following could represent the graph of $f(x)$.

2. Section 3.2 Graphing using the second derivative. Concavity. Second derivative test. Inflection points, sketching given the sign diagrams. I could ask a question such as: If $f''(x) = x-2$, which of the following could represent the graph of $f(x)$.

3. Section 3.3, 3.4 & 3.5 Absolute max's and min's on a closed or open interval. A variety of optimization problems. You should be able to do the homework story problems that were assigned. Major types include Area/Perimeter problems, Profit, Revenue with $x$= number of $10 reductions, optimal lot size, tax revenue, and others. In some cases, I may ask you just to set up the problem.

4. Section 3.6 Implicit differentiation and using it to find dy/dx. Basic related rates problems.

5. Section 4.1 Exponential functions, $e^x$, interest rate problems with compounding. Present value problems, depreciation, domain and range.

6. Section 4.2 Logarithmic functions, domain and range, log rules, time to double, triple, etc. C-14 dating.

7. Section 4.3 Derivatives of natural logarithms and exponentials. Related story problems.

8. Section 4.4 Relative rates of change and elasticity of demand problems. You will need to remember these formulas on your own.

9. Section 8.1 Radians to degrees, degrees to radians, co-terminal angles, arc length.

10. Section 8.2 Definition of sin and cos with triangles and the unit circle. Finding these values in other quadrants. Finding these values using your calculator (degrees or radians). A couple story problems. A very basic trig identity, $\sin^2(x) + \cos^2(x) = 1$. Basic Graphing or identifying graphs.

11. Section 8.3 Derivatives of sine and cosine and related story problems.

12. Section 8.5 Other trig functions and their derivatives. You only need to memorize the derivative of $\tan(x)$.

The exam is not yet completed, but I anticipate the test looking very similar to the homework problems. There may be a couple of extra questions that aren't homework questions, but knowing how to do all of the homework will prepare you very well. Obviously, you should also read through the text and notes as well.