# Math 190: Study Guide - Chapter 3

- Use the rules of differentiation to find and simplify the derivative of
the function. These could involve the power rule, addition rule, multiplication
rule, quotient rule, and chain rule. Nine parts. Look at the problems in
sections 3.1, 3.2, and 3.3.
- Find the derivative of the function but do NOT simplify the results. Three
parts. Look at the same problems as question 1, but these are not as pretty
and you can waste a lot of time simplifying and still not have a nice looking
answer.
- Given a table with values for x, f(x), f'(x), g(x), and g'(x), evaluate
each of the derivatives asked for. For example, if you are asked to find
d/dx [ f(x)g(x) ] |
_{x=2}, then you would use the product rule to
find f(x)g'(x) + f'(x)g(x) and then since this is evaluated when x=2, you
get f'(2)g(2)+f'(2)g(2). Look each of those values up in the table, substitute
them into the expression, and evaluate. Five parts.
- Given a demand and cost function, find the revenue and profit functions;
the marginal cost, marginal revenue, and marginal profit functions; evaluate
the marginal functions at a particular point and interpret. Finally, find
the average cost. Look at problems 3.4.3-17.
- Find the elasticity of demand. The formula for elasticity of demand is
provided on the exam. Then determine the regions where the function is elastic,
inelastic, and unitary. Look at problems 3.4.23-34.
- Use a local linear approximation with a differential to approximate an
expression. Look at problems 3.7.19-26.
- Find the first and second derivatives of the function. Two parts. Look
at problems 3.5.1-20.
- Find the first and second derivatives of a function at a specific point
and interpret within the context of the story. Look at problems 3.5.29-38.

## 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.

## Points per problem

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
Total |

Pts |
36 |
12 |
15 |
12 |
6 |
5 |
8 |
6 |
100 |