## Math 190 - Chapter 4 Study Guide

1. Sketch a graph that has the given characteristics. Two parts. Look at problems 4.3.32 - 4.3.35.
2. Find the intervals where the function is increasing and decreasing. Find any relative maximums or relative minimums. Two parts. One polynomial function, one rational function. Look at problems 4.1.10 - 4.1.35 and 4.1.48 - 4.1.71.
3. Find the intervals where the function is concave up and concave down. Find any points of inflection. Two parts. One polynomial function, one rational function. Look at problems 4.2.22 - 4.2.73.
4. Given a function, find its domain, vertical asymptotes, horizontal asymptotes, x-intercepts, y-intercepts, intervals where increasing, intervals where decreasing, intervals where concave up, intervals where concave down, relative maximums, relative minimums, points of inflection and sketch the graph of the function. Look at problems 4.3.36 - 4.3.59.
5. Find the absolute maximum and the absolute minimum of the function on the interval. Look at problems 4.4.9 - 4.4.38. Two parts. One polynomial function, one rational function.
6. True or False. Eight parts. Know the definitions of critical point, point of inflection. Know when critical points and points of inflection occur. Know the first derivative test and the second derivative test. Know when absolute maximums and minimums occur.
7. Optimization problem. Look at problems 4.4.39 - 4.4.51, 4.4.59. Use your calculator to find the absolute maximum and minimum.
8. Optimization problem. Look at problems 4.5.3 - 4.5.13. You will need to know some geometry formulas for surface area and volume of right solids.

### Notes

• None of the problems are directly from the text. They are of the kind of problem shown in each section.
• The application problems are similar to problems in the text, but the numbers have been changed.