Question

Find the average rate of change for f(x) = x2
+ 9x + 18 from x = 10 to x = 20.
Responses
A 3333
B 3737
C 3939
D 41

Answer 1

To find the average rate of change of the function \( f(x) = x^2 + 9x + 18 \) from \( x = 10 \) to \( x = 20 \), we will use the formula for the average rate of change:

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

where \( a = 10 \) and \( b = 20 \).

1. First, calculate \( f(10) \):
\[
f(10) = 10^2 + 9(10) + 18 = 100 + 90 + 18 = 208
\]

2. Next, calculate \( f(20) \):
\[
f(20) = 20^2 + 9(20) + 18 = 400 + 180 + 18 = 598
\]

3. Now substitute \( f(10) \) and \( f(20) \) into the average rate of change formula:
\[
\text{Average Rate of Change} = \frac{f(20) - f(10)}{20 - 10} = \frac{598 - 208}{10} = \frac{390}{10} = 39
\]

Thus, the average rate of change of the function \( f(x) \) from \( x = 10 \) to \( x = 20 \) is \( 39 \).

Therefore, the correct answer is:
**C 39**.