select the correct answer. if f(x)=x³ - x, what is the average rate of change of f(x) over the interval 1…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 1$, $b = 5$, and $f(x)=x^{3}-x$.

Step2: Calculate $f(5)$

Substitute $x = 5$ into $f(x)$: $f(5)=5^{3}-5=125 - 5=120$.

Step3: Calculate $f(1)$

Substitute $x = 1$ into $f(x)$: $f(1)=1^{3}-1=1 - 1=0$.

Step4: Calculate the average rate of change

$\frac{f(5)-f(1)}{5 - 1}=\frac{120-0}{4}=\frac{120}{4}=30$.

Answer:

B. 30