Question

Find the average rate of change of the function f left parenthesis x right parenthesis equals 9 x from x 1 equals 0 to x 2 equals 2.
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Part 1
The average rate of change is
  
enter your response here. ​(Simplify your​ answer.)

Answer 1

To find the average rate of change of the function \( f(x) = 9x \) from \( x_1 = 0 \) to \( x_2 = 2 \), we can use the formula for the average rate of change:

\[
\text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
\]

First, we need to evaluate \( f(x) \) at \( x_1 \) and \( x_2 \).

1. Calculate \( f(0) \):
\[
f(0) = 9 \cdot 0 = 0
\]

2. Calculate \( f(2) \):
\[
f(2) = 9 \cdot 2 = 18
\]

Now we can apply these values to the formula:

\[
\text{Average Rate of Change} = \frac{f(2) - f(0)}{2 - 0} = \frac{18 - 0}{2 - 0} = \frac{18}{2} = 9
\]

Thus, the average rate of change of the function \( f(x) = 9x \) from \( x = 0 \) to \( x = 2 \) is:

\[
\boxed{9}
\]