Math 121 - Chapters 4-5 Study Guide

1. Find dy/dx by implicit differentiation. Two parts. Look at problems 4.3.11-20*.
2. Find d²y/dx² by implicit differentiation. Look at problems 4.3.21-26*.
3. Find the derivatives of the inverse trigonometric functions. Three parts. Two of these were worked out in class.
4. Use the graph of y=f(x) to find the intervals on which f is increasing, decreasing, concave up, and concave down. Also give the x-coordinates of all points of inflection. Look at problem 5.1.7.
5. Related rate application problem. Look at problems 4.6.7-25*
6. Related rate application problem. Look at problem 4.6.42.
7. Sketch a continuous curve that has the stated properties. Two parts. Look at problem 5.1.31.
8. Locate the critical points, and classify them as stationary points or points of non-differentiability. Two parts. Look at problems 5.2.7-12*.
9. Classify each critical point as a relative maximum, relative minimum, or neither. Five parts. Know the first and second derivative tests to answer these.
10. Give a complete graph of the polynomial and label the coordinates of the intercepts, stationary points, and inflection points. Check your work with a graphing utility. Look at problems 5.3.1-10*.
11. Give a complete graph of the function and identify the location of all critical points and inflection points. Check your work with a graphing utility. Look at problems 5.3.25-32*.
12. Given a polynomial function in factored form, answer the following questions. Nine parts. Look on pages 308-310.
1. When roots are counted according to their multiplicity, how many real or complex zeros are there?
2. What is the right hand behavior of the graph?
3. What is the left hand behavior of the graph?
4. What is the maximum number of relative extrema possible?
5. What are the x-intercepts of the function?
6. Where will the graph cross the x-axis?
7. Where will the graph touch the x-axis?
8. Where will the graph be tangent to the x-axis?
9. Where will the graph have an inflection point on the x-axis?

Notes:

• Starred problems are directly from the text.