4. Space Science. A rocket is shot vertically into the air. Its height in ft at any time t, in seconds, can be determined by the function What is the maximum height it will achieve during it’s flight?

18. The time at which the rocket will reach it’s maximum height The maximum height that the rocket will achieve

19. The time at which the rocket will reach it’s maximum height The maximum height that the rocket will achieve What is the maximum height it will achieve during it’s flight?

21. Minimizing Cost. Aki’s Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by where C(x) is in hundreds of dollars. How many bicycles should be built in order to minimize the average cost per bicycle?

34. The number of bicycles (in hundreds) that should be built to minimize cost The minimum average cost (in hundreds of dollars) 350 $120

35. The number of bicycles (in hundreds) that should be built to minimize cost The minimum average cost (in hundreds of dollars) 350 $120 How many bicycles should be built in order to minimize the average cost per bicycle?

36. bicycles The number of bicycles (in hundreds) that should be built to minimize cost The minimum average cost (in hundreds of dollars) 350 $120 How many bicycles should be built in order to minimize the average cost per bicycle?

38. Maximizing Area. A fourth-grade class decides to enclose a rectangular garden, using the side of the school as one side of the rectangle. What is the maximum area that the class can enclose with 32 ft of fence? What should the dimensions of the garden be in order to yield this area? SCHOOL Let x = the length of the side

39. Maximizing Area. A fourth-grade class decides to enclose a rectangular garden, using the side of the school as one side of the rectangle. What is the maximum area that the class can enclose with 32 ft of fence? What should the dimensions of the garden be in order to yield this area? SCHOOL Let x = the length of the side

40. Maximizing Area. A fourth-grade class decides to enclose a rectangular garden, using the side of the school as one side of the rectangle. What is the maximum area that the class can enclose with 32 ft of fence? What should the dimensions of the garden be in order to yield this area? SCHOOL Let x = the length of the side

41. SCHOOL

43. Descending order

44. SCHOOL

45. Maximizing Area. A fourth-grade class decides to enclose a rectangular garden, using the side of the school as one side of the rectangle. What is the maximum area that the class can enclose with 32 ft of fence? What should the dimensions of the garden be in order to yield this area?

46. , SCHOOL

48. The length of the side that achieves the maximum area The maximum area than can be achieved

49. The length of the side that achieves the maximum area What is the maximum area that the class can enclose with 32 ft of fence? The maximum area than can be achieved SCHOOL

50. The length of the side that achieves the maximum area What is the maximum area that the class can enclose with 32 ft of fence? The maximum area than can be achieved SCHOOL

51. The length of the side that achieves the maximum area What should the dimensions of the garden be in order to yield this area? The maximum area than can be achieved SCHOOL

52. The length of the side that achieves the maximum area The maximum area than can be achieved What should the dimensions of the garden be in order to yield this area? SCHOOL

53. The length of the side that achieves the maximum area The maximum area than can be achieved What should the dimensions of the garden be in order to yield this area? SCHOOL

54. The length of the side that achieves the maximum area The maximum area than can be achieved What should the dimensions of the garden be in order to yield this area? SCHOOL

55. What should the dimensions of the garden be in order to yield this area? SCHOOL

57. 4. Finding Maximizing Area: Among all the rectangles whose perimeters are 100 ft., find the dimensions of the one with maximum area.

58. Let x = the length of the side

59. Divide between two Remaining sides

60. Divide between two Remaining sides

65. Descending order

67. 4. Finding Maximizing Area: Among all the rectangles whose perimeters are 100 ft., find the dimensions of the one with maximum area.

68. ,

70. The length of the side that achieves the maximum area The maximum area than can be achieved

71. The length of the side that achieves the maximum area Find the dimensions of the one with maximum area The maximum area than can be achieved

72. The length of the side that achieves the maximum area The maximum area than can be achieved Find the dimensions of the one with maximum area