Math 190: Study Guide - Chapters 4-5

1. A function and its first two derivatives are given to you in factored form. Make sign charts for f, f', and f". Give intervals where the function is postive, negative, increasing, decreasing, concave up, and concave down. Give any x-intercepts, relative maximums, relative minimums, and inflection points.
2. The graph of a function and its derivative are given on the same coordinate system. Determine which is the function and which is the derivative. Four parts. Look at problems 4.1.43-46 and 4.3.29-30.
3. The graph of a function is given. Sketch the graph of the derivative of the same coordinate system. Two parts.
4. A continuous function with exactly one critical point is given. Determine whether there is a relative maximum, a relative minimum, neither a relative maximum or a relative minimum, not enough information is given to determine whether or not there is a relative extremum, or the situation is impossible. You will need to know the first and second derivative tests. Ten parts.
5. The graph of a function is given. Make sign charts for f, f', and f".
6. The graph of the derivative of a function is given. Make sign charts for f' and f". Determine where there are relative maximums, relative minimums, and inflection points for the original graph.
7. Sketch a function that has the given characteristics. Two parts. Look at problems 4.3.33-36.
8. Find the absolute maximum and absolute minimum of the function on the closed interval. Look at problems 4.4.15-28.
9. Know the properties of logarithms and use the supplied table of logarithms to find the values of the logarithms asked for. For example, if logb 2 = 3.8018 and logb 3 = 6.0257, then logb 6 = logb (2·3) = logb 2 + logb 3 = 3.8018 + 6.0257 = 9.8275. Three parts. Look at problems 5.2.11-16.
10. Solve the exponential or logarithmic equations for x. Give exact answers. Four parts. Look at problems 5.1.17-26, 5.3.35-44.
11. Find the derivative of the exponential or logarithmic functions. Eight parts. Look at problems 5.5.1-32.
12. Find the second derivative of the exponential or logarithmic functions. Two parts. Look at problems 5.5.33-36.
13. An exponential model is given. Use it to answer the questions. Look at problems 5.6.13-22.

Notes

• Show work if there is any. In a very few cases, you may be able to do the problem in your head.
• You will need your calculator for this exam.
• Most of the problems from chapter 4 are visual in nature or have already had the derivatives found for you. The focus is on whether you understand what the derivatives mean rather than how to find the derivatives. This is different from most places in the book where you had to find the derivative and then interpret it, so it is difficult to find problems in the book like all of the problems on the test.

Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 Total 13 4 6 10 6 7 10 4 6 8 16 4 6 100