Answer :
The rate of change over the interval is the difference in the y coordinate over the difference in x-coordinate over between the endpoints of the interval.
[tex]\text{rate of change =}\frac{\Delta y}{\Delta x}[/tex]Now, in our case
[tex]\frac{\Delta y}{\Delta x}=\frac{y(5)-y(2)}{5-2}[/tex][tex]=\frac{\sqrt[]{5-1}-\sqrt[]{2-1}}{5-2}[/tex][tex]=\frac{2-1}{5-2}=\frac{1}{3}[/tex][tex]\therefore\text{rate of change }=\frac{1}{3}\text{.}[/tex]Hence, choice C is correct.