Answer
$\frac{7}{3}$
Work Step by Step
Given the interval [2,3]
f(3)=$\frac{3^{2}}{2}+\frac{1}{3}=\frac{29}{6}$
f(2)=$\frac{2^{2}}{2}+\frac{1}{2}=\frac{5}{2}$
The average rate of change of f(x) over the interval [2,3]
$\frac{f(3)−f(2)}{3−2}=\frac{\frac{29}{6}-\frac{15}{6}}{1}=\frac{7}{3}$
