What is the average rate of change for g(x)=(x+2)^2-9 from x=1 to x=4?

9

Step-by-step explanation:

Expand. (x+2)^2-9=x^2+4x-5. For x=1, the function equals 1^2+4*1-5=0.

4^2+4*4-5=16+16-5=27.

(27-0)/3= 9

Step-by-step explanation:

9

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.

christopher is 272,195 year old

step-by-step explanation: