Math 148 Review for Test (chapters 1-10)
The test will cover chapters 1-10, but there will be more emphasis on chapters 8, 9, 10. There will be two parts. On part 1, no graphing calculator is allowed. It will have questions where you have to use derivatives to find when a function is increasing, decreasing, and find max and min points. Part 2 will have all the other questions, and you may use a graphing calculator.
Chapters 1-7
The questions will be similar to the quiz
Chapter 8
1. derivatives
2. critical points
3. using the derivative to find maximum, minimum, and when a function is increasing and decreasing
Chapter 9
1. using solver to find maximum and minimum points. See sample question #9 below
Chapter 10
1. anti-derivatives
2. finding area under the curve (using rectangles, and also using anti-derivatives)
3. consumer surplus and not-sold region (explain the concept, and calculate the area)
Sample Questions
For additional sample questions, see “Exam Practice” at www.wamap.org for our class.
1) (no graphing calculator allowed for this question) Consider the function
a) find f ' (x)
b) find all the critical points
c) for each critical point found in part (b), determine if it is a minimum, a maximum, or neither
d) determine the intervals where f(x) is increasing
e) determine the intervals where f(x) is decreasing
2) Consider the function f(x) = 4x2 + 3x - 8
a) find f ' (x)
b) What is the instantaneous rate of change when x = 3?
3) Suppose the Sunglasses Hut Company has a profit function given by
P(q) = -0.02q2 + 6q - 26, where q is the number of thousands of pairs of sunglasses sold and produced, and P(q) is the total profit, in thousands of dollars, from selling and producing pairs of sunglasses.
a) Find a simplified expression for the marginal profit function.
b) How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your answer to three decimal places.)
4) Consider the function f(x) = 10x8 + 9x7 - 10x3 - 6
Give the anti-derivative F(x) (make sure to add + C)
5) Evaluate the definite integral:
6) Let f(x) = x2 + 4. The graph is shown on the right: /
a) Use 4 rectangles and the midpoint formula to estimate the area under the curve of f(x) from x = 2 to x = 10. Include a sketch of the rectangles on the graph above.
b) Use the anti-derivative to compute the exact area in problem (a)
7) Here is a graph of a demand curve,(q is number of units and D(q) is US Dollars) /
a) Let q = 300. Estimate the actual revenue if 300 units are sold. Shade in this area in the graph above.
b) Assume 300 units are sold. Shade in this area in the graph above that represents the consumer surplus (but do not compute)
8) Below is a graph of f(x)
a) At what point (A, B, or C) is f ‘ (x) < 0 ?
b) At what point (A, B, or C) is f ‘ (x) = 0 ?
9) A closed rectangular box whose volume is 324 cubic inches is to be made with a square base. If the material for the bottom costs twice as much per square inch as the sides and top, find the dimensions of the box that minimize the cost of materials.
a) Write the function for the cost of the box
b) What is the constraint?
c) Show what you would enter in cells A2 through D2, and then in the Solver Box in order to solve this problem.
A / B / C / D1 / x / y / cost / volume
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