Question

find the average rate of change of the function on the interval specified. g(x) = 6x^3 - 8 on -3, 3

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = g(x)$ on the interval $[a,b]$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a=-3$, $b = 3$, and $g(x)=6x^{3}-8$.

Step2: Calculate $g(3)$

Substitute $x = 3$ into $g(x)$: $g(3)=6\times3^{3}-8=6\times27 - 8=162-8 = 154$.

Step3: Calculate $g(-3)$

Substitute $x=-3$ into $g(x)$: $g(-3)=6\times(-3)^{3}-8=6\times(-27)-8=-162 - 8=-170$.

Step4: Calculate the average rate of change

$\frac{g(3)-g(-3)}{3-(-3)}=\frac{154-(-170)}{3 + 3}=\frac{154 + 170}{6}=\frac{324}{6}=54$.

Answer:

54