#### Answer

$\frac{1}{3}$

#### Work Step by Step

y = $\sqrt x$ between x = 1 and x = 4
To find the rate of change, you have to use the rate of change formula:
$\frac{f(b)âˆ’f(a)}{bâˆ’a}$
In this problem, the starting point is 1 and the end point is 4. Therefore, a = 1 and b = 4.
Since you know the a and b values, you can plug them into the formula:
$\frac{(\sqrt 4)-(\sqrt 1)}{4-1}$
= $\frac{2-1}{3}$
= $\frac{1}{3}$
Therefore, the average rate of change is equal to $\frac{1}{3}$