1. Average and Instantaneous Rate of Change

2. B
f(a +h) ­ f(a)
distance
A
h
a a + h
time
f(a+h) ­ f(a)
average velocity =
h

3. B
B
f(a +h) ­ f(a)
distance B
A
tangent line
a a + h
time
Instantaneous rate of change: lim f (a + h) ­ f(a)
h 0
h

4. Find the slope of the tangent line at x = 1 on f(x) = x2.

5. Find the slope of the tangent line at x = 1 on f(x) = x2.
now let x 0

6. THE DEFINITION lim f(x + h) ­ f(x)
h 0
OF THE DERIVATIVE h
f (a + h) ­ f(a)
f (a) = lim
'
h 0
h

7. Find the derivative of f(x) = x2

8. Exercise 2.2
questions 1 ­ 15
odd numbers