Find the average rate of change of the function \( f(x)=x^{2}+9 x \) from \( x_{1}=2 \) to \( x_{2}=7 \). The average rate of change is \( \square \). (Simplify your answer.)

To find the average rate of change of the function \( f(x) = x^2 + 9x \) from \( x_1 = 2 \) to \( x_2 = 7 \), we use the formula: \[ \text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \] First, we calculate \( f(2) \) and \( f(7) \): \[ f(2) = 2^2 + 9(2) = 4 + 18 = 22 \] \[ f(7) = 7^2 + 9(7) = 49 + 63 = 112 \] Now, we can plug these values into the formula: \[ \text{Average Rate of Change} = \frac{112 - 22}{7 - 2} = \frac{90}{5} = 18 \] Thus, the average rate of change is \( 18 \).