find the average rate of change of the function f(x)=7x from x1 = 0 to x2 = 6. the average rate of change is…
find the average rate of change of the function f(x)=7x from x1 = 0 to x2 = 6. the average rate of change is □. (simplify your answer.)
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 $f(x_1)$ and $f(x_2)$
Given $f(x)=7x$, $x_1 = 0$ and $x_2=6$. Then $f(x_1)=f(0)=7\times0 = 0$ and $f(x_2)=f(6)=7\times6 = 42$.
Step3: Substitute values into formula
$\frac{f(x_2)-f(x_1)}{x_2 - x_1}=\frac{42 - 0}{6-0}=\frac{42}{6}$.
Step4: Simplify the result
$\frac{42}{6}=7$.
Answer:
7