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.)

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1. The average rate of change (AROC) of a function $$ f(x) $$ from $$ x_1 $$ to $$ x_2 $$ is given by:
   $$
   \text{AROC} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}.
   $$

2. Given $$ f(x) = x^2 + 9x $$, substitute $$ x_1 = 2 $$ and $$ x_2 = 7 $$:
   
   - First, compute $$ f(2) $$:
     $$
     f(2) = (2)^2 + 9(2) = 4 + 18 = 22.
     $$
   
   - Then, compute $$ f(7) $$:
     $$
     f(7) = (7)^2 + 9(7) = 49 + 63 = 112.
     $$

3. Now, substitute into the AROC formula:
   $$
   \text{AROC} = \frac{112 - 22}{7 - 2} = \frac{90}{5} = 18.
   $$

4. The average rate of change of the function from $$ x=2 $$ to $$ x=7 $$ is $$ \boxed{18} $$.
The average rate of change is 18.

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.)

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