8. what is the average rate of change of the function f given by f(x)=x^4 - 5x on the closed interval 0,3…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0$, $b = 3$, and $f(x)=x^{4}-5x$.

Step2: Calculate $f(3)$

Substitute $x = 3$ into $f(x)$: $f(3)=3^{4}-5\times3=81 - 15=66$.

Step3: Calculate $f(0)$

Substitute $x = 0$ into $f(x)$: $f(0)=0^{4}-5\times0 = 0$.

Step4: Calculate the average rate of change

Using the formula $\frac{f(b)-f(a)}{b - a}$, we have $\frac{f(3)-f(0)}{3 - 0}=\frac{66-0}{3}=22$.

Answer:

C. 22