3. Average Rate vs. Instantaneous Rate
Graphically
a b
Average Rate of Change
Between a and b
Instantaneous Rate of
Change at a
4. Average Rate of Change
Between x = a & x = b
a b
f(a)
f(b)
b - a
f(b) – f(a)
f(b) – f(a)
b - a
= Slope of the line
5. Instantaneous Rate at x = a
a =3 a+h= 3.01
Instantaneous Rate of
Change at a
Use a =3, h = 0.01
h= 0.01
f(a)= f(3)
f(a+h)=f(3.01)
f(3.01)-f(3)
3.01- 3
f (3.01)- f(3)
3.01 - 3
=
6. 1 3 4
2
f(1)
a) f (1)
b) f (4)- f(3)
f (4)- f(3)
c) f (4)- f(3)
4 - 3
f (4)- f(3)
4 - 3
Find: Average Rate of
Change between
x=3 and x=4
Inst. Rate of
Change at x = 1
7.
8.
9.
10.
11.
12.
13.
14. Estimate the instantaneous rate of change for the function
below when x = 1, using the nearby point (2, 5).
Use the points (1, 0) and (2, 5), both on the
graph, to find the slope of the secant.
slope = 5− 0
2 − 1
= 5
Based on the selected interval, the instantaneous
rate of change is estimated to be 5.
22. A cyclist is observed moving at a speed of 10 m/s. She begins
to slow down at a constant rate and, 4 s later, is at a speed of 5
m/s. She continues to slow down at a different constant rate
and finally comes to a stop 6 s later.
a) Sketch a graph of speed versus time.
b) What is the average rate of change of the cyclist’s speed in
the first 4 s?
c) Estimate the instantaneous rate of change in speed at 3 s.
