1. Warm up 8/26 Warm up 1. Do in notebook True or False, if false explain why or give example 1. If, then 2. If, then 3. If, then 4. If, then

2. 1. 2. 3. 4.

3. Homework Group Check in with your group! See which problems you have questions on Help your group member. Still unsure ? Thank about what you need to ask. Write those questions down. - Go over as a class.

4. Before the quiz: Group Study questions : When do you use the c-definition over the delta x? How to you find equations of tangent lines? What are the import parts, and how do you get them? How to you find equations of secant lines ? What is the derivative and what are some of its notations?

5. Be seated before the bell rings DESK homework Warm-up (in your notes) Agenda : warm-up / go over hw Hw Quiz Notes lesson 2.2 continues

6. Notebook Table of content Page 1 Learning Target 1 1)1-1 A Preview of Calculus 2) 1-2 Finding limits graphically and numerically 3) 1-3 Evaluating limits analytically 4) 1-4 Continuity 5) 1-5 & 3.5 6) 2.1 The Derivative 7)2.2 The power rule Learning Target LT2: I can use the power HW: P 116; 97-104

7. 2.2 continues Motions Problems Where ?How fast ?Accelerations milesmi/hr Derivative : Rate 1) Position, displacement 2) velocity Forward Distance increase backward Toward start, Speed How fast with no directions 3) Acceleration: change in velocity PVAPVA

8. PVAPVA EX: 1) Velocity equation? 2) Acceleration equation? 3) Where is the object when t = o? 4) How fast are we going when t = o? 5) How fast the object is going when it hits the ground.

9. PVAPVA EX: 6) When does the object have no velocity ? 7) What is the average velocity t = 0, t = 1.

10. Free falling objects A ball is dropped from a height of 100 feet. What is it position function?

11. Free falling objects At time t = 0, a diver jumps from a platform diving board that is 32 feet above the water He had an initial Velocity of 16 feet per second, What is it position function?

12. Example 10 – Using the Derivative to Find Velocity At time t = 0, a diver jumps from a platform diving board that is 32 feet above the water Because the initial Velocity of the diver is 16 feet per second, the position of the diver is s(t) = –16t 2 + 16t + 32 Position function where s is measured in feet and t is measured in seconds. a.When does the diver hit the water? b. What is the diver’s velocity at impact? Figure 2.21

13. Example 10(a) – Solution To find the time t when the diver hits the water, let s = 0 and solve for t. –16t 2 + 16t + 32 = 0 Set position function equal to 0. –16(t + 1)(t – 2) = 0 Factor. t = –1 or 2 Solve for t. Because t ≥ 0, choose the positive value to conclude that the diver hits the water at t = 2 seconds.

14. Example 10(b) – Solution The velocity at time t is given by the derivative s(t) = –32t + 16. So, the velocity at time is t = 2 is s(2) = –32(2) + 16 = –48 feet per second. cont’d

17. 102