what is the average rate of change of the function below on the interval 0, 0.3? f(x)=-7x³/(x⁴ - 1) 0.609…

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, $a = 0$, $b=0.3$, and $f(x)=\frac{-7x^{3}}{x^{4}-1}$.

Step2: Calculate $f(0)$

Substitute $x = 0$ into $f(x)$: $f(0)=\frac{-7\times0^{3}}{0^{4}-1}=0$.

Step3: Calculate $f(0.3)$

Substitute $x = 0.3$ into $f(x)$: $f(0.3)=\frac{-7\times(0.3)^{3}}{(0.3)^{4}-1}=\frac{-7\times0.027}{0.0081 - 1}=\frac{-0.189}{- 0.9919}\approx0.1905$.

Step4: Calculate average rate of change

Using the formula $\frac{f(b)-f(a)}{b - a}$, we have $\frac{f(0.3)-f(0)}{0.3-0}=\frac{0.1905 - 0}{0.3}=0.635$.

Answer:

0.635