Question

quiz 5 (3.2, 3.3, 3.4)
score: 1.79/6 answered: 2/6
question 3
find the average rate of change of $g(x)=4x^{3}-2$ from $x = - 4$ to $x = 1$.
question help: message instructor

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, $a=-4$, $b = 1$, and $g(x)=4x^{3}-2$.

Step2: Calculate $g(a)$

Substitute $x=-4$ into $g(x)$:
$g(-4)=4\times(-4)^{3}-2=4\times(-64)-2=-256 - 2=-258$.

Step3: Calculate $g(b)$

Substitute $x = 1$ into $g(x)$:
$g(1)=4\times(1)^{3}-2=4 - 2=2$.

Step4: Calculate the average rate of change

Use the formula $\frac{g(b)-g(a)}{b - a}=\frac{2-(-258)}{1-(-4)}=\frac{2 + 258}{1 + 4}=\frac{260}{5}=52$.

Answer:

52