1. So that’s what he's thinking about 3.4

2. Original Function 1 st Derivative 2 nd Derivative 3 rd Derivative

3. Time Distance Velocity

4. Suppose a rock is thrown straight up from atop a 200 - meter-high cliff at an initial speed of 30 feet per second. The height, in meters, of the rock above the ground (until it lands) at time t is given by the function h(t) = - 4.905t 2 + 30t + 200. When does the rock reach its maximum height? What is this maximum height? How fast is the rock moving after 3 seconds? How fast does the rock hit the ground?

5. Suppose a rock is thrown straight up from atop a 200 - meter-high cliff at an initial speed of 30 feet per second. The height, in meters, of the rock above the ground (until it lands) at time t is given by the function h(t) = - 4.905t 2 + 30t + 200. When does the rock reach its maximum height? At the rocks maximum height the velocity will be zero Time (seconds) Height (meters)

6. Suppose a rock is thrown straight up from atop a 200 - meter-high cliff at an initial speed of 30 feet per second. The height, in meters, of the rock above the ground (until it lands) at time t is given by the function h(t) = - 4.905t 2 + 30t + 200. When does the rock reach its maximum height? Time (seconds) Height (meters) What is this maximum height? To find the maximum height plug in 3.06 for x in the height equation h(t)

7. Suppose a rock is thrown straight up from atop a 200 - meter-high cliff at an initial speed of 30 feet per second. The height, in meters, of the rock above the ground (until it lands) at time t is given by the function h(t) = - 4.905t 2 + 30t + 200. When does the rock reach its maximum height? Time (seconds) Height (meters) What is this maximum height? How fast is the rock moving after 3 seconds?

8. Suppose a rock is thrown straight up from atop a 200 - meter-high cliff at an initial speed of 30 feet per second. The height, in meters, of the rock above the ground (until it lands) at time t is given by the function h(t) = - 4.905t 2 + 30t + 200. Time (seconds) Height (meters) How fast does the rock hit the ground? Find the x-intercepts using the calculator or the quadratic formula then plug into v(t) 10.138 -69.5 m/sec

9. A dynamic blast propels a heavy rock straight up with a launch velocity 200 ft/sec. It reaches a height of s = 200t - 16t 2 after t seconds. When does the rock reach its maximum height? What is this maximum height? How fast is the rock moving after 7seconds? How fast does the rock hit the ground?

10. A dynamic blast propels a heavy rock straight up with a launch velocity 200 ft/sec. It reaches a height of s = 200t - 16t 2 after t seconds. When does the rock reach its maximum height? What is this maximum height?

11. A dynamic blast propels a heavy rock straight up with a launch velocity 200 ft/sec. It reaches a height of s = 200t - 16t 2 after t seconds. How fast is the rock moving after 7seconds?

12. A dynamic blast propels a heavy rock straight up with a launch velocity 200 ft/sec. It reaches a height of s = 200t - 16t 2 after t seconds. How fast is the rock moving when it hits the ground?

13. Time (seconds) Distance The graph gives the distance a particle travels on a number line starting at 0. Describe the particles movement from 0 – 11 seconds 0 sec - 4 sec 4 sec – 5 sec 5 sec – 7 sec 7 sec – 8 sec 8 sec – 10 sec 10 sec – 11 sec Moving to the right at 1 unit/sec Moving to the right at 3 units/sec At rest Moving to the left at 2 units/sec Moving to the left at 0.5 unit/sec Moving to the left at 4 units/sec 1 2 3 4 5 6 7 8 9 10 11 7 6 5 2 1

14. Time (seconds) Distance The graph gives the distance a particle travels on a number line starting at 6 units. Describe the particles movement from 0 – 11 seconds 0 sec - 3 sec 3 sec – 6 sec 6 sec – 7 sec 7 sec – 11 sec Moving to the left at 4/3 units/sec At rest Moving to the right at 2 units/second Moving to the left at 1 unit/sec 1 2 3 4 5 6 7 8 9 10 11 7 6 5 2 1

15. Time (sec) Velocity (units/sec) The graph gives the velocity of a particle that travels on a number line starting at 0. Describe the particles movement from 0 – 11 seconds. 0-2 seconds 2-4 seconds 4-6 seconds 6-7 seconds 7-9 seconds 9-11 1 2 3 4 5 6 7 8 9 10 11 The particle is accelerating at 1 unit/sec 2 to the right The particle maintains a constant speed of 2 units/second The particle is decelerating at 1 unit/sec 2 until the it comes to rest after 6 seconds The particle accelerates at 1 unit/sec 2 to the left. The particle maintains a constant speed of 1 unit/sec to the left The particle decelerates at ½ unit/sec 2 until it comes to rest

16. Time (sec) Velocity (units/sec) The graph gives the velocity of a particle that travels on a number line starting at 0. Describe the particles movement from 0 – 11 seconds. 0-2 seconds 2-4 seconds 4-6 seconds 7-8 seconds 8-10 seconds 9-10 1 2 3 4 5 6 7 8 9 10 11 The particle is accelerating at 3/2 unit/sec 2 to the left. The particle decelerates at ½ units/sec 2 The particle remains at a constant speed of 2 units per second to the left. The particle decelerates at 2 unit/sec 2. The particle is at rest The particle accelerates at 1 unit/sec 2 to the right.