in the interval
[tex]3\le x\le6[/tex]we can see that
[tex]\begin{gathered} \text{when x=3, y=f(x)=10} \\ \text{when x=6, y=f(x)=12} \end{gathered}[/tex]the average rate of change is the slope m. The formula for m is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where
[tex]\begin{gathered} (x_1,y_1)=(3,10) \\ \text{and} \\ (x_2,y_2)=(6,12) \end{gathered}[/tex]By substituying these values, we have
[tex]m=\frac{12-10}{6-3}[/tex]hence,
[tex]m=\frac{2}{3}[/tex]Therefore, the average rate of change is 2/3=0.667
