Question

Find the average rate of change of the function

Answer 1

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.

Answer 2

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

$\dfrac{f(x_2)-f(x_1)}{x_2-x_1}$

Let's find the values of $f(x_1)$ and $f(x_2)$

$f(x_1)=4^2+3(4)=28$
$f(x_2)=9^2+3(9)=108$

$\dfrac{f(x_2)-f(x_1)}{x_2-x_1}$

$=\dfrac{108-28}{9-4}=\boxed{16}$

Your answer is 16. I hope this helps and have an awesome day! :)