# Math 190: Study Guide - Chapter 3

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. Use a local linear approximation with a differential to approximate an expression. Look at problems 3.7.19-26.
7. Find the first and second derivatives of the function. Two parts. Look at problems 3.5.1-20.
8. 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

 # Pts 1 2 3 4 5 6 7 8 Total 36 12 15 12 6 5 8 6 100