what is the average rate of change of the function $g(x) = 3x^2 - 2x$ on the interval from $x = -2$ to $x = 4$?

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Accepted Answer

# Explanation:
## Step1: Recall the average rate of change formula
The average rate of change of a function $ g(x) $ on the interval $[a, b]$ is given by $\frac{g(b)-g(a)}{b - a}$. Here, $ a=-2 $ and $ b = 4 $.

## Step2: Calculate $ g(-2) $
Substitute $ x=-2 $ into $ g(x)=3x^{2}-2x $:
$$
\begin{align*}
g(-2)&=3(-2)^{2}-2(-2)\
&=3\times4 + 4\
&=12 + 4\
&=16
\end{align*}
$$

## Step3: Calculate $ g(4) $
Substitute $ x = 4 $ into $ g(x)=3x^{2}-2x $:
$$
\begin{align*}
g(4)&=3(4)^{2}-2(4)\
&=3\times16-8\
&=48 - 8\
&=40
\end{align*}
$$

## Step4: Calculate the average rate of change
Using the formula $\frac{g(4)-g(-2)}{4-(-2)}$, substitute $ g(4) = 40 $ and $ g(-2)=16 $:
$$
\begin{align*}
\frac{g(4)-g(-2)}{4-(-2)}&=\frac{40 - 16}{4 + 2}\
&=\frac{24}{6}\
&=4
\end{align*}
$$

# Answer:
4

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the average rate of change formula

Step2: Calculate \( g(-2) \)

Step3: Calculate \( g(4) \)

Step4: Calculate the average rate of change

Answer: