What is the average rate of change of the function f(x) on the interval 6 < x < 8

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.