## Math 121 - Chapters 4-5 Study Guide

- Find dy/dx by implicit differentiation. Two parts. Look at problems 4.3.11-20*.
- Find d
^{2}y/dx^{2} by implicit differentiation. Look at problems 4.3.21-26*.
- Find the derivatives of the inverse trigonometric functions. Three parts. Two of these were
worked out in class.
- 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.
- Related rate application problem. Look at problems 4.6.7-25*
- Related rate application problem. Look at problem 4.6.42.
- Sketch a continuous curve that has the stated properties. Two parts. Look at problem 5.1.31.
- Locate the critical points, and classify them as stationary points or points of non-differentiability. Two parts. Look at problems 5.2.7-12*.
- Classify each critical point as a relative maximum, relative minimum, or neither. Five parts.
Know the first and second derivative tests to answer these.
- 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*.
- 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*.
- Given a polynomial function in factored form, answer the following questions. Nine parts.
Look on pages 308-310.
- When roots are counted according to their multiplicity, how many real or complex
zeros are there?
- What is the right hand behavior of the graph?
- What is the left hand behavior of the graph?
- What is the maximum number of relative extrema possible?
- What are the x-intercepts of the function?
- Where will the graph cross the x-axis?
- Where will the graph touch the x-axis?
- Where will the graph be tangent to the x-axis?
- Where will the graph have an inflection point on the x-axis?

### Notes:

- Starred problems are directly from the text.

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
Total |

Pts |
10 |
5 |
9 |
10 |
6 |
6 |
10 |
10 |
10 |
8 |
8 |
9 |
101 |