1. 2.2C Derivative as a Rate of Change

2. Average Velocity: the slope of the secant line between [a, b] on a position curve s(t).

3. Instantaneous Velocity: the slope of the tangent line to a point (a, s(a)) on a position curve.

4. That is … f(x) = the slope of the tangent line at x
s(a) = the velocity at t = a
| s(a)| = the speed at t = a

5. Ex 1: t: min 36 38 40 42 44 s(t): Heartbeats
2530
2661
2806
2948
3080
Use the data to calculate the slope of the secant line between each of the given points and the point: (42, 2948).

6. Ex 1: Estimate the slope of the tangent line @ t = 42 min
Find the equation of the tangent t = 42 min

7. Ex 2: C(x): where C = cost in dollars & x = fabric in yards
What are the units of C(x)? What does C(1000) = 9 mean?

8. Ex 3: The displacement (meters) of a particle moving in a straight line is given where t is seconds.

9. Ex 3: a) Find the average velocity. on the interval [4, 4
Ex 3: a) Find the average velocity on the interval [4, 4.5] b) Find the instantaneous velocity at x = 4

10. 2.2C pg. 117 # 89 – 95 odds, # 97 – 100 all, 107, 113

11. Ex 4: a) Find the velocity & speed of the particle after 2 seconds.
s: meters
t: seconds

12. Ex 4: b) Will the particle ever stop? If so, when?
s: meters
t: seconds

13. Ex 4: c) When is the particle moving away from its starting point?
s: meters
t: seconds

14. The derivative of f at x is f’(x):