Respuesta :

The average rate of change from an interval from [tex]x_1[/tex] to [tex]x_2[/tex] is the change in the value of the function divided by the change in x.

[tex]\dfrac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

Let's find the values of [tex]f(x_1)[/tex] and [tex]f(x_2)[/tex]

[tex]f(x_1)=4^2+3(4)=28[/tex]
[tex]f(x_2)=9^2+3(9)=108[/tex]

[tex]\dfrac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

[tex]=\dfrac{108-28}{9-4}=\boxed{16}[/tex]

Your answer is 16. I hope this helps and have an awesome day! :)
Average rate of change=change in f(x)/ change in x=(f(x₂)-f(x₁)) / (x₂-x₁)
Data:
f(x)=x²+3x
x₁=4
x₂=9

Average rate of change=((9²+3*9) - (4²+3*4)) / (9-4)=
=((81+27)-(16+12)) / (9-4)=
=(108-28)/5=80/5=16.

Answer: The average rate of change is 16.

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