Question

watch the video and then solve the problem given below. click here to watch the video. find the average rate of change of the function $f(x)=x^{2}+3x$ from $x_1 = 1$ to $x_2 = 5$. the average rate of change is \\(\square\\). (simplify your answer.)

Explanation:

Step1: Define average rate formula

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

Step2: Calculate $f(x_1)$ where $x_1=1$

$f(1) = 1^2 + 3(1) = 1 + 3 = 4$

Step3: Calculate $f(x_2)$ where $x_2=5$

$f(5) = 5^2 + 3(5) = 25 + 15 = 40$

Step4: Substitute into the formula

$\frac{f(5)-f(1)}{5-1} = \frac{40-4}{5-1} = \frac{36}{4}$

Step5: Simplify the fraction

$\frac{36}{4} = 9$

Answer:

9