1. Average Rate vs. Instantaneous Rate
Average Rate of Change Between a and b
Instantaneous Rate of Change at a a b

2. Average Rate of Change Between x = a & x = b
f(b) – f(a) b - a
= Slope of the line
f(b)
f(b) – f(a)
f(a)
b - a a b

3. Average Rate vs. Instantaneous Rate
Average Rate of Change Between a and b
Instantaneous Rate of Change at a a b

4. Instantaneous Rate at x = a
Use a =3, h = 0.01
Instantaneous Rate of Change at a
f (3.01)- f(3) =
f(a+h)=f(3.01)
f(3.01)-f(3)
f(a)= f(3)
h= 0.01
a =3
a+h= 3.01

5. Find: a) f ‘ (1) f (4)- f(3) 4 - 3 b) f (4)- f(3) c) f (4)- f(3) 4 - 3
Average Rate of Change between x=3 and x=4
a) f ‘ (1)
f (4)- f(3)
b) f (4)- f(3)
c) f (4)- f(3)
f (4)- f(3)
Inst. Rate of Change at x = 1
f ‘ (1)
f(1) 1 2 3 4

6. The Constant Rule If f(x) is constant, the derivative is 0. 5 -8 -6 -4-8 -6 -4 -2 2 4 6 8 -5

7. The Linear Rule
If f(x) is a linear function, the derivative is its own slope. 5 -8 -6 -4 -2 2 4 6 8 -5