We can find the average rate of change with the following formula
[tex]\frac{f(b)-f(a)}{b-a}[/tex]Which is defined inside the interval
[tex]a\leq x\leq b[/tex]In other words, this formula allows us to calculate the average rate of change inside the interval [a,b], which in this case is [4,7].
First, we find f(a) and f(b):
[tex]\begin{gathered} f(4)=4^2+9=16+9=25 \\ f(5)=5^2+9=25+9=34 \end{gathered}[/tex]Now, we use the formula
[tex]\frac{34-25}{7-4}=\frac{9}{3}=3[/tex]