The average rate of change of [tex]f[/tex] over an interval [tex][a,b][/tex] is the difference quotient
[tex]\dfrac{f(b) - f(a)}{b - a}[/tex]
Over the interval [tex]3\le x\le5[/tex], we have
[tex]\dfrac{f(5) - f(3)}{5 - 3} = \dfrac{27 - 3}{5 - 3} = \dfrac{24}2 = \boxed{12}[/tex]
