Question

practice assignment 3.3 rates of change and i
find the average rate of change of $g(x)=-4x^{3}-1$ from $x = - 4$ to $x = 4$.
question help: video message instructor post to forum

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = g(x)$ from $x = a$ to $x = b$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a=-4$, $b = 4$, and $g(x)=-4x^{3}-1$.

Step2: Calculate $g(-4)$

Substitute $x=-4$ into $g(x)$:
$g(-4)=-4\times(-4)^{3}-1=-4\times(-64)-1 = 256 - 1=255$.

Step3: Calculate $g(4)$

Substitute $x = 4$ into $g(x)$:
$g(4)=-4\times4^{3}-1=-4\times64 - 1=-256-1=-257$.

Step4: Calculate the average rate of change

$\frac{g(4)-g(-4)}{4-(-4)}=\frac{-257 - 255}{4 + 4}=\frac{-512}{8}=-64$.

Answer:

$-64$