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

User CLAbeel
by
4.5k points

1 Answer

11 votes

Answer:

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.

User Ali Hesari
by
4.3k points