Average rate of change over an interval is defined as:
[tex]\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]The interval define is :
[tex]2\leq x\leq6[/tex]This implies that the average rate of change over the interval is:
[tex]\begin{gathered} \frac{f(x_6)-f(x_2)}{x_6-x_1}=\text{ }\frac{19-13}{6-2} \\ \\ \text{The average rate of change over the interval=}\frac{6}{4}=\frac{3}{2} \end{gathered}[/tex]Hence, the average rate of change over the interval is;
[tex]\frac{3}{2}[/tex]