Constant Rule
Power Rule
d
[c] = 0
dx
d
[xn] = nx(n­1)
dx
Constant Multiple Rule
d
[cf(x)] = cf '(x)
dx
Sum and Differences Rule
d
[f(x) + g(x)] = f '(x) + g '(x)
dx
d
[f(x) ­ g(x)] = f '(x) ­ g '(x)
dx
Title: Sep 12­9:54 AM (1 of 5)
Rates of Change
Position function ­ the function s that gives the position of an object as a function of time t
Rate = distance
time
Average Velocity:
Change in Distance
Change in Time
Title: Sep 14­8:57 AM (2 of 5)
=
Example: A billiard ball is dropped from a height of 100 feet, its height s at time t is given by the position function
where s is measured in feet and t is measured in seconds. Find the average velocity over each of the following time intervals.
a. [1, 2]
Title: Sep 14­9:06 AM (3 of 5)
b. [1, 1.5]
c. [1, 1.1]
Instantaneous Velocity
In general, if s = s(t) is the position function for an object moving along a straight line, then the velocity of the object at time t is
Title: Sep 14­9:03 AM (4 of 5)
Example: At t = 0 a diver jumps from a platform diving board that is 32 feet above the water.
The position of the diver is given by a. When does the diver hit the water?
b. What is the diver's velocity at impact?
Title: Sep 14­9:18 AM (5 of 5)