a b c d e GOOD LUCK! 3. a b c d e 12. a b c d e 4. a b c d e 13. a b c d e 5. a b c d e 14. a b c d e 6. a b c d e 15. a b c d e

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1 MA Elem. Calculus Spring 07 Eam Name: Sec.: Do not remove this answer page you will turn in the entire eam. No books or notes may be used. You may use an ACT-approved calculator during the eam, but NO calculator with a Computer Algebra System (CAS), networking, or camera is permitted. Absolutely no cell phone use during the eam is allowed. The eam consists of two short answer questions and eighteen multiple choice questions. Answer the short answer questions on the back of this page, and record your answers to the multiple choice questions on this page. For each multiple choice question, you will need to ll in the circle corresponding to the correct answer. It is your responsibility to make it CLEAR which response has been chosen. For eample, if (a) is correct, you must write a b c d e You have two hours to do this eam. Please write your name on this page, and at the top of page three. GOOD LUCK!. a b c d e. a b c d e 4. a b c d e. a b c d e 5. a b c d e 4. a b c d e 6. a b c d e 5. a b c d e 7. a b c d e 6. a b c d e 8. a b c d e 7. a b c d e 9. a b c d e 8. a b c d e 0. a b c d e 9. a b c d e. a b c d e 0. a b c d e For grading use: Multiple Choice Short Answer Total (number right) (5 points each) (out of 0 points) (total 00 points)

2 Name: Last 4 digits of Student ID: Spring 07 Eam Short Answer Questions Write answers on this page. Your work must be clear and legible to be sure you will get full credit. y f,4. Sketch the graph of a continuous function for which f is increasing on decreasing on, and ; on. 4, f 0 on, 7, f 0,7,. Suppose we know two nonnegative numbers and y satisfying y. Find the maimum possible value of their product y. You must clearly use calculus to find and justify your answer. Your final answer does not need to be simplified. Maimum possible product:

3 Name: Multiple Choice Questions Show all your work on the page where the question appears. Clearly mark your answer both on the cover page on this eam and in the corresponding questions that follow.. Where is the function f(t) = t + 6t 6t + 8 decreasing? (a) t < (b) f(t) is always decreasing (c) 6 < t < (d) t > (e) t < 6 and t > 4. Where is the function f(t) = concave up? t 5 (a) f(t) is never concave up (b) < t < 5 (c) t < 5 (d) t > 5 (e) f(t) is always concave up ecept at t = 5

4 5. Suppose the derivative of g(t) is g 0 (t) = (t ) (t 7). For t in which interval(s) is g increasing? (a) ( ; ) [ (7; ) (b) ( ; 7) (c) (; 7) (d) (; 7) [ (; ) (e) (7; ) 6. Suppose the derivative of g(t) is g 0 (t) = 8 t. Where is the function g(t) concave up? (a) f(t) is always concave up (b) t < 9 and t > 9 (c) t < 0 (d) 9 < t < 9 (e) t > 0 4

5 7. The following is the graph of the derivative, f 0 (), of the function f(). Where is the original function f() decreasing? (a) nowhere (b) ( ; ) (c) everywhere ( ) y = f 4 y the derivative (d) (; ) (e) ( ; ) this graph shows the derivative 8. The following is the graph of the derivative, f 0 (), of the function f(). Where is the original function f() concave up? (a) nowhere (b) (; ) (c) ( ; ) ( ) y = f 4 y the derivative (d) ( ; ) (e) everywhere this graph shows the derivative 5

6 9. A farmer builds a rectangular pen with 8 vertical partitions (9 vertical sides) using 400 feet of fencing. What is the maimum possible total area of the pen? (a) 000 (b) 400 (c) 0000 (d) (e) A car rental agency rents 90 cars per day at a rate of $7 dollars per day. For each dollar increase in the daily rate, fewer cars are rented. At what rate should the cars be rented to produce maimum income? (a) $44:57 per day (b) $45:7 per day (c) $44:77 per day (d) $45:7 per day (e) $45:97 per day 6

7 . Find the critical numbers of the function f() = e +. (a) ; 0 (b) 0 (c) (d) (e) ; 0; e. Given the function f() =( if < 0 if 0 Z evaluate the denite integral 80 f() d 90 (a) 750 (b) 0 (c) 850 (d) 4450 (e) 850 7

8 . The graph of y = f() shown below consists of straight lines. Evaluate the denite integral R f() d: (a) 7:5 (b) :5 (c) 6 (d) :5 (e) : y 4-4. The graph of y = f() shown below includes semicircles and a straight line. Evaluate the denite integral f() d: Use = :4. R4 (a) 7:85 (b) 9:4 4 y (c) 4:7 (d) 7:85 (e) 4:

9 5. Suppose that R7 5 (a) 9 (b) 5 (c) 5 (d) 9 (e) 5 f() d = andr7 6 f() d = 7. Find the value of R5 f() d Suppose that R (a) 504 (b) 8 (c) 544 (d) 94 (e) 96 7 f() d = 9 and R g() d = 9. Find the value of R (f() + 4g()) d

10 7. Find the average value of f() on the interval [, ] given that f() =(90 if < 6 0 if 6: 5 (a) (b) 55 (c) 6 (d) 0 (e) Estimate the area under the graph of + 0 for between and 4, by using a partition that consists of 4 equal subintervals of [; 4] and use the right endpoint of each subinterval as a sample point. (a) 70 (b) 06 (c) 54 (d) 98 (e) 008 0

11 9. Suppose you estimate the area under the graph of f() = from = 5 to = 45 by adding the areas of the rectangles as follows: partition the interval into 0 equal subintervals and use the right endpoint of each interval to determine the height of the rectangle. What is the area of the 0th rectangle? (a) 5 (b) ln () + ln (5) (c) :0464 (d) (e) 5 0. Suppose you are given the following data points for a function f(). 4 f() If f is a linear function on each interval between the given points, nd R4 f() d. (a) 4 (b) 45 (c) 9 (d) (e) 5

12 Some Formulas. Areas: (a) Triangle A = bh (b) Circle A = r (c) Rectangle A = lw (d) Trapezoid A = h + h. Volumes: b (a) Rectangular Solid V = lwh (b) Sphere (c) Cylinder V = 4 r V = r h (d) Cone V = r h

13 MA Elem. Calculus Spring 07 Eam Name: Sec.: Do not remove this answer page you will turn in the entire eam. No books or notes may be used. You may use an ACT-approved calculator during the eam, but NO calculator with a Computer Algebra System (CAS), networking, or camera is permitted. Absolutely no cell phone use during the eam is allowed. The eam consists of two short answer questions and eighteen multiple choice questions. Answer the short answer questions on the back of this page, and record your answers to the multiple choice questions on this page. For each multiple choice question, you will need to ll in the circle corresponding to the correct answer. It is your responsibility to make it CLEAR which response has been chosen. For eample, if (a) is correct, you must write a b c d e You have two hours to do this eam. Please write your name on this page, and at the top of page three. GOOD LUCK!. a b c d e. a b c d e 4. a b c d e. a b c d e 5. a b c d e 4. a b c d e 6. a b c d e 5. a b c d e 7. a b c d e 6. a b c d e 8. a b c d e 7. a b c d e 9. a b c d e 8. a b c d e 0. a b c d e 9. a b c d e. a b c d e 0. a b c d e For grading use: Multiple Choice Short Answer Total (number right) (5 points each) (out of 0 points) (total 00 points)