Find the average rate of change of the function \( f(x)=\sqrt{x} \) from \( x_{1}=4 \) to \( x_{2}=49 \). The average rate of change is \( \square \). (Simplify your answer.)

To find the average rate of change of the function \( f(x) = \sqrt{x} \) from \( x_1 = 4 \) to \( x_2 = 49 \), we use the formula: \[ \text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \] First, we calculate \( f(x_1) \) and \( f(x_2) \): \[ f(4) = \sqrt{4} = 2 \] \[ f(49) = \sqrt{49} = 7 \] Now, substituting these values into the formula: \[ \text{Average Rate of Change} = \frac{7 - 2}{49 - 4} = \frac{5}{45} = \frac{1}{9} \] Thus, the average rate of change is \( \frac{1}{9} \).