find the average rate of change of g(x) = x³ - 16x + 20 over the interval -6, -1. write your answer as an integer, fraction, or decimal rounded to the nearest tenth. simplify any fractions.

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for average rate of change
The average rate of change of a function $ g(x) $ over the interval $[a, b]$ is given by $\frac{g(b) - g(a)}{b - a}$. Here, $ a=-6 $ and $ b = - 1 $.

## Step2: Calculate $ g(-6) $
Substitute $ x=-6 $ into $ g(x)=x^{3}-16x + 20 $:
$$
\begin{align*}
g(-6)&=(-6)^{3}-16\times(-6)+20\
&=-216 + 96+20\
&=-216+116\
&=-100
\end{align*}
$$

## Step3: Calculate $ g(-1) $
Substitute $ x = - 1 $ into $ g(x)=x^{3}-16x + 20 $:
$$
\begin{align*}
g(-1)&=(-1)^{3}-16\times(-1)+20\
&=-1 + 16+20\
&=35
\end{align*}
$$

## Step4: Calculate the average rate of change
Using the formula $\frac{g(b)-g(a)}{b - a}$ with $ a=-6 $, $ b=-1 $, $ g(-6)=-100 $ and $ g(-1) = 35 $:
$$
\begin{align*}
\frac{g(-1)-g(-6)}{-1-(-6)}&=\frac{35-(-100)}{-1 + 6}\
&=\frac{35 + 100}{5}\
&=\frac{135}{5}\
&=27
\end{align*}
$$

# Answer:
$ 27 $

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for average rate of change

Step2: Calculate \( g(-6) \)

Step3: Calculate \( g(-1) \)

Step4: Calculate the average rate of change

Answer: