## Math 121 - Chapter 3 Study Guide

- For the accompanying position versus time graph, find the average velocity over an interval,
the places where the instantaneous velocity is zero, the times at which the instantaneous
velocity is a maximum or minimum, and the instantaneous velocity at a specific time. Look at
problem 3.1.10.
- Match the graphs of the functions with the graphs of their derivatives. Five parts. Look at
problem 3.2.23.
- Sketch the graph of the derivative of the function whose graph is shown. Look at problems
3.2.25-26
- Find the derivative. Four parts. Look at problems 3.3.1-28.
- Find f'(x) for trigonometric functions. Four parts. Look at problems 3.4.1-18.
- Find f'(x) using the chain rule. Four parts. Look at problems 3.5.1-39.
- Find the derivatives as the specified point. Six parts. Look at supplementary exercise 3.10.
- Find the differential dy. Look at problems 3.6.9-12.
- Use the limit definition of the derivative (Definition 3.2.2) to find the derivative of the given
function. Look at problems 3.2.9-14. Note: 9-14 ask for the equation of the tangent line, I'm
just asking for the derivative. Also note that this is a problem where I will be grading work
more than the answer. Be sure you write the limit in every time until you actually take the
limit.
- Use a local linear approximation to estimate the value given. Look at problems 3.6.27-35.
- Find a higher order derivative. Look at problems 3.3.41-44.
- True / false statements regarding continuity and differentiability of functions. Two parts.
- Write formulas for the slope of a secant line and the slope of a tangent line. Two parts.

### Notes:

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
Tot. |

Pts |
8 |
5 |
4 |
16 |
16 |
16 |
12 |
3 |
6 |
4 |
4 |
2 |
4 |
100 |