You have the following function:
[tex]f(x)=2x^2-4x+9[/tex]
Take into account that the average rate of change is given by the following formula:
[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
where x1 and x2 are the limits of a given interval.
In this case, you have x1 = 0 and x2 = 9. Replace these values to calculate f(0) and f(9):
[tex]\begin{gathered} f(0)=2(0)^2-4(0)+9=9 \\ f(9)=2(9)^2-4(9)+9=2(81)-36+9=162-36+9=135 \end{gathered}[/tex]
Next, replace the previous results into the formula for m:
[tex]m=\frac{135-9}{9-0}=\frac{126}{9}=14[/tex]
Hence, the average rate of change is 14
