Question

find the average rate of change of the function $f(x)=x^{2}+2x$ from $x_{1}=3$ to $x_{2}=5$. the average rate of change is \square. (simplify your answer.)

Explanation:

Step1: Compute $f(x_1)$ where $x_1=3$

$f(3) = 3^2 + 2(3) = 9 + 6 = 15$

Step2: Compute $f(x_2)$ where $x_2=5$

$f(5) = 5^2 + 2(5) = 25 + 10 = 35$

Step3: Apply average rate formula

$\text{Average rate of change} = \frac{f(x_2)-f(x_1)}{x_2-x_1} = \frac{35-15}{5-3} = \frac{20}{2}$

Step4: Simplify the result

$\frac{20}{2} = 10$

Answer:

10