Question

find the average rate of change of the function f(x)=x^2 + 3x from x_1 = 2 to x_2 = 4. the average rate of change is . (simplify your answer.)

Explanation:

Step1: Find f(x1)

Substitute \(x_1 = 2\) into \(f(x)=x^{2}+3x\).
\[f(2)=2^{2}+3\times2=4 + 6=10\]

Step2: Find f(x2)

Substitute \(x_2 = 4\) into \(f(x)=x^{2}+3x\).
\[f(4)=4^{2}+3\times4=16+12 = 28\]

Step3: Calculate average rate of change

The formula for the average rate of change of a function from \(x_1\) to \(x_2\) is \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\).
\[

$$\begin{align*} \frac{f(4)-f(2)}{4 - 2}&=\frac{28-10}{4 - 2}\\ &=\frac{18}{2}\\ &=9 \end{align*}$$

\]

Answer:

9