Find the average rate of change of g(x) = 1x3 + 2 from x =
1 to x = 4

Step-by-step explanation:

Explanation:

The

average rate of change

of g(x) over an interval between 2 points (a ,g(a)) and (b ,g(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

g

(

b

)

−

g

(

a

)

b

−

a

a

a

∣

∣

∣

−−−−−−−−−−−−−−−

g

(

6

)

=

6

2

−

6

+

3

=

33

and

g

(

4

)

=

4

2

−

4

+

3

=

15

Thus the average rate of change between (4 ,15) and (6 ,33) is

33

−

15

6

−

4

=

18

2

=

9

This means that the average of all the slopes of lines tangent to the graph of g(x) between (4 ,15) and (6 ,33) is 9