question 8 5 pts 1 details find the average rate of change of g(x)=2x³ + 4 from x = -1 to x = 4. enter an…

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

Step2: Calculate $g(-1)$

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

Step3: Calculate $g(4)$

Substitute $x = 4$ into $g(x)$: $g(4)=2(4)^{3}+4=2\times64 + 4=128+4=132$.

Step4: Calculate the average rate of change

Using the formula $\frac{g(b)-g(a)}{b - a}$, we have $\frac{g(4)-g(-1)}{4-(-1)}=\frac{132 - 2}{4 + 1}=\frac{130}{5}=26$.

Answer:

26