Answer:
Step-by-step explanation:
The
average rate of change
of f(x) over an interval between 2 points (a ,f(a)) and (b ,f(b)) is the slope of the
secant line
connecting the 2 points.
To calculate the average rate of change between the 2 points use.
∣
∣
∣
∣
∣
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
a
a
f
(
b
)
−
f
(
a
)
b
−
a
a
a
∣
∣
∣
−−−−−−−−−−−−−−−
f
(
9
)
=
9
2
−
6
(
9
)
+
8
=
35
and
f
(
4
)
=
4
2
−
6
(
4
)
+
8
=
0
The average rate of change between (4 ,0) and (9 ,35) is
35
−
0
9
−
4
=
35
5
=
7
This means that the average of all the slopes of lines tangent to the graph of f(x) between (4 ,0) and (9 ,35) is 7.
