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Calculus An Applied Approach 9th Edition Test Bank Ron Larson

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1. Use the graph of to identify at which of the indicated points the derivative changes from positive to negative.

A) (5,6)
B) (-1,2), (5,6)
C) (2,4)
D) (2,4), (5,6)
E) (-1,2)
Ans: A

2. Use the graph of to identify at which of the indicated points the derivative changes from negative to positive.

A) (2,4)
B) (-1,2)
C) (-1,2), (5,6)
D) (5,6)
E) (2,4), (5,6)
Ans: B

3. Identify the open intervals where the function is increasing or decreasing.
A) decreasing: ; increasing:
B) increasing: ; decreasing:
C) increasing on
D) decreasing on
E) none of the above
Ans: A

4. Both a function and its derivative are given. Use them to find all critical numbers.

A)
B)
C)
D)
E)
Ans: D

5. Identify the open intervals where the function is increasing or decreasing.
A) increasing: ; decreasing:
B) decreasing: ; increasing:
C) increasing on
D) decreasing on
E) none of the above
Ans: A

6. For the given function, find all critical numbers.

A)
B) and
C) and
D) and
E) and
Ans: D

7. Find any critical numbers of the function , t < 5. A) 0 B) C) D) both A and B E) both A and C Ans: C 8. Identify the open intervals where the function is increasing or decreasing. A) decreasing: ; increasing: B) increasing: ; decreasing: C) increasing: ; decreasing: D) increasing: ; decreasing: E) decreasing for all x Ans: B 9. For the given function, find the critical numbers. A) B) C) D) E) Ans: A 10. Find the open intervals on which the function is increasing or decreasing. A) The function is increasing on the interval , and decreasing on the intervals and . B) The function is increasing on the interval , and decreasing on the intervals and . C) The function is increasing on the interval , and decreasing on the intervals and . D) The function is decreasing on the interval , and increasing on the intervals and . E) The function is decreasing on the interval , and increasing on the intervals and . Ans: A 11. Find the open intervals on which the function is increasing or decreasing. A) The function is increasing on the interval and decreasing on the interval . B) The function is increasing on the interval and decreasing on the interval . C) The function is increasing on the interval and decreasing on the interval . D) The function is increasing on the interval and decreasing on the interval . E) The function is increasing on the interval and decreasing on the interval . Ans: E 12. Suppose the number y of medical degrees conferred in the United States can be modeled by for , where t is the time in years, with corresponding to 1975. Use the test for increasing and decreasing functions to estimate the years during which the number of medical degrees is increasing and the years during which it is decreasing. A) The number of medical degrees is increasing from 1975 to 1992 and 2000 to 2005, and decreasing during 1992 to 2000. B) The number of medical degrees is increasing from 1975 to 1991 and 1999 to 2005, and decreasing during 1991 to 1999. C) The number of medical degrees is increasing from 1975 to 1992 and 1999 to 2005, and decreasing during 1992 to 1999. D) The number of medical degrees is increasing from 1975 to 1993 and 1999 to 2005, and decreasing during 1993 to 1999. E) The number of medical degrees is increasing from 1975 to 1992 and 1998 to 2005, and decreasing during 1992 to 1998. Ans: C 13. A fast-food restaurant determines the cost model, and revenue model, for where x is the number of hamburgers sold. Determine the intervals on which the profit function is increasing and on which it is decreasing. A) The profit function is increasing on the interval and decreasing on the interval . B) The profit function is increasing on the interval and decreasing on the interval . C) The profit function is increasing on the interval and decreasing on the interval . D) The profit function is increasing on the interval and decreasing on the interval . E) The profit function is increasing on the interval and decreasing on the interval . Ans: C 14. For the given function, find the relative minima. A) B) C) D) E) no relative minima Ans: B 15. Find the x-values of all relative maxima of the given function. A) B) C) D) E) no relative maxima Ans: D 16. For the function : (a) Find the critical numbers of f (if any); (b) Find the open intervals where the function is increasing or decreasing; and (c) Apply the First Derivative Test to identify all relative extrema. Then use a graphing utility to confirm your results. A) (a) x = 0 , 6 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 6 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 2 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 2 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 2 (b) increasing: ; decreasing: (c) relative max: ; no relative min. Ans: A 17. Find all relative maxima of the given function. A) B) C) D) , E) no relative maxima Ans: B 18. Find all relative minima of the given function. A) B) C) D) , E) no relative minima Ans: D 19. Locate the absolute extrema of the function on the closed interval . A) no absolute max; absolute min: f(1) = 5 B) absolute max: f(2) = 22 ; absolute min: f(1) = 5 C) absolute max: f(1) = 5 ; no absolute min D) absolute max: f(1) = 5 ; absolute min: f(2) = 22 E) no absolute max or min Ans: D 20. Locate the absolute extrema of the function on the closed interval [0,5]. A) absolute max: f(5) = 65 ; absolute min: f(2) = 16 B) absolute max: f(2) = 16 ; absolute min: f(5) = 65 C) absolute max: f(5) = 65 ; no absolute min D) no absolute max; absolute min: f(5) = 65 E) no absolute max or min Ans: A 21. Find the x-value at which the absolute minimum of f (x) occurs on the interval [a, b]. A) B) C) D) E) Ans: A 22. Locate the absolute extrema of the given function on the closed interval [36,36]. A) absolute max: f(6) = 3 B) absolute min: f(-6) = 3 C) no absolute max D) no absolute min E) both A and D F) both A and B Ans: F 23. Find the absolute extrema of the function on the closed interval . Round your answer to two decimal places. A) The maximum of the function is 1 and the minimum of the function is 0. B) The maximum of the function is 2.92 and the minimum of the function is 1. C) The maximum of the function is 2.92 and the minimum of the function is 0. D) The maximum of the function is1 and the minimum of the function is 2.08. E) The maximum of the function is 0 and the minimum of the function is 2.08. Ans: C 24. Approximate the critical numbers of the function shown in the graph and determine whether the function has a relative maximum, a relative minimum, an absolute maximum, an absolute minimum, or none of these at each critical number on the interval shown. A) The critical number yields an absolute maximum and the critical number yields an absolute minimum.. B) Both the critical numbers & yield an absolute maximum. C) The critical number yields an absolute minimum and the critical number yields an absolute maximum. D) Both the critical numbers and yield an absolute minimum. E) The critical number yields a relative minimum and the critical number yields a relative maximum. Ans: C 25. Find the absolute extrema of the function on the interval . A) The maximum of the function is 1 and the minimum of the function is 0. B) The maximum of the function is 0 and the minimum of the function is 10. C) The maximum of the function is 10 and the minimum of the function is 0. D) The maximum of the function is 10 and the minimum of the function is 0. E) The maximum of the function is 0 and the minimum of the function is 10. Ans: D 26. Graph a function on the interval having the following characteristics. Absolute maximum at Absolute minimum at Relative maximum at Relative minimum at A) B) C) D) E) Ans: A 27. Medication. The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by . Find the t-value at which x is maximum. Round your answer to two decimal places. A) 0 hours B) 2.24 hours C) 894.43 hours D) 4.24 hours E) 5.46 hours Ans: B 28. Medication. The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by . Find the maximum value of x. Round your answer to two decimal places. A) 2.65 mg B) 755.93 mg C) 1663.04 mg D) 8.20 mg E) 1500.40 mg Ans: B 29. Suppose the resident population P(in millions) of the United States can be modeled by , where corresponds to 1800. Analytically find the minimum and maximum populations in the U.S. for . A) The population is minimum at and maximum at . B) The population is minimum at and maximum at . C) The population is minimum at and maximum at . D) The population is minimum at and maximum at . E) The population is minimum at and maximum at . Ans: D 30. Determine the open intervals on which the graph of is concave downward or concave upward. A) concave upward on ; concave downward on B) concave downward on C) concave upward on D) concave downward on ; concave upward on E) concave upward on ; concave downward on Ans: C 31. Determine the open intervals on which the graph of is concave downward or concave upward. A) concave downward on B) concave downward on ; concave upward on C) concave upward on ; concave downward on D) concave downward on ; concave upward on E) concave upward on ; concave downward on Ans: E 32. Find all relative extrema of the function . Use the Second Derivative Test where applicable. A) relative min: B) relative max: C) no relative max D) no relative min E) both A and C F) both B and D Ans: E 33. Find all relative extrema of the function Use the Second Derivative Test where applicable. A) relative max: ; no relative min B) relative max: ; no relative min C) no relative max or min D) relative min: ; no relative max E) relative min: ; no relative max Ans: E 34. Find all relative extrema of the function . Use the Second Derivative Test where applicable. A) relative max: f(1) = 6 B) relative min: f(0) = 7 C) no relative max or min D) both A and B E) none of the above Ans: B 35. Find all relative extrema of the function . Use the Second-Derivative Test when applicable. A) The relative minimum is and the relative maximum is . B) The relative maximum is . C) The relative minimum is . D) The relative maximum is and the relative minima are and . E) The relative minimum is and the relative maximum is . Ans: B 36. Find all relative extrema of the function . Use the Second-Derivative Test when applicable. A) The relative maximum is . B) The relative minimum is . C) The relative maximum is . D) The relative minimum is . E) The relative maximum is . Ans: C 37. State the signs of and on the interval (0, 2). A) = 0 > 0
B) < 0 < 0 C) > 0
> 0
D) < 0 > 0
E) > 0

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