Question

find the average rate of change of the function f(x)=x^2 + 7x from x_1 = 3 to x_2 = 4.
the average rate of change is . (simplify your answer.)

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x_1$ to $x_2$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$.

Step2: Calculate $f(x_1)$

Given $f(x)=x^{2}+7x$ and $x_1 = 3$, then $f(3)=3^{2}+7\times3=9 + 21=30$.

Step3: Calculate $f(x_2)$

Given $x_2 = 4$, then $f(4)=4^{2}+7\times4=16+28 = 44$.

Step4: Calculate the average rate of change

Substitute $f(x_1)=30$, $f(x_2)=44$, $x_1 = 3$, and $x_2 = 4$ into the formula: $\frac{f(4)-f(3)}{4 - 3}=\frac{44 - 30}{1}=14$.

Answer:

14