Math 117 Review Sheet for Quiz (Chapters 1-5)

Math 148 Review sheet for Quiz (chapters 1-7)

The quiz will cover chapters 1-7. Problems will be similar to the online homework. Practice these questions (click “try another similar question” after a problem to make a new problem for more practice). There will be a few topics that did not have online homework, listed below. Make sure you can do problems related to the following topics:

Chapter 1 Basic vocabulary and business background information

Chapter 2 1. Using Excel to graph equations. 2. Cost functions 3. Piecewise functions

Chapter 3 1. given some raw data, decide what type of function would best fit the data. 2. demand functions

Chapter 4 1. given information about costs and demand, find the revenue and profit functions. 2. use demand, revenue, cost, and/or profit functions to answer questions (such as what is the profit when q = 150) 3. finding the break-even point

Chapter 5 1. Limit problems

Chapter 6 and 7 1. Find and interpret average rate of change 2. Find and interpret instantaneous rate of change

Sample questions:

1. If you wanted to graph the function f(x) = x 1 over the interval [0,10]. Show what you would enter cells B2 and B3:

A B 1 x F(x) 2 0 3 0.1

x 2 1 if x  4 2. Make a graph of f(x) =  x  3 if x  4 3. The fixed cost is $24 million, and the first 200,000 units cost $53 each to produce. After that, the rest of the units cost $49 each to produce. Make a cost function, where q represents thousands of units, and C(q) represents millions of dollars.

4. The following data gives the price per unit vs. number of units sold. What type of function would best represent this data? Explain your answer. units 25 30 35 40 45 50 price $ 6.51 $ 5.68 $ 5.01 $ 4.56 $ 4.01 $ 3.56

5. If the fixed cost is $4,900 and the variable cost is $4 per unit, and if the demand function is D(q) = -0.01q + 40: a) what is the revenue function? b) what is the profit function? c) what would be the profit if 50 units were sold? d) how many units would you have to sell to make a profit of $400?

x 2  9 6. Find lim x3 x  3 7. Consider the function f(x) = 4x2 + 5x – 2

a) What is the average rate of change from x = -2 to x = 0 b) Estimate the instantaneous rate of change, using the forward method, at the point where x = 3 c) Estimate the instantaneous rate of change, using the forward-backward method, at the point where x = 3. Let h = 0.1

8. Suppose the revenue function for a product is R(q) = -2q3 + 4q2 + 3q, where q is in thousands and revenue is in millions. a) Estimate the marginal revenue, using the forward-backward method, for 2,000 units. b) Explain what the answer to part (a) means. Include units with your answer.