what is the average rate of change of the function below on the interval -4, -3? f(x)=-1/x³ 0.021 0.028…

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

Step2: Calculate $f(-4)$ and $f(-3)$

$f(-4)=-\frac{1}{(-4)^{3}}=\frac{1}{64}$; $f(-3)=-\frac{1}{(-3)^{3}}=\frac{1}{27}$.

Step3: Substitute into the formula

$\frac{f(-3)-f(-4)}{-3-(-4)}=\frac{\frac{1}{27}-\frac{1}{64}}{1}=\frac{64 - 27}{27\times64}=\frac{37}{1728}\approx0.021$.

Answer:

0.021