find the average rate of change of g(x) = 3x³ − 5x² between x = −0.2 and x = 0.2. enter the exact answer. the average rate of change of g(x) between x = −0.2 and x = 0.2 is

Question

Accepted Answer

# Answer:
-0.2
# Explanation:
## Step1: Recall the formula for average rate of change
The average rate of change of a function $ g(x) $ between $ x = a $ and $ x = b $ is given by $ \frac{g(b)-g(a)}{b - a} $. Here, $ a=- 0.2$ and $ b = 0.2$.

## Step2: Calculate $ g(-0.2) $
Substitute $ x=-0.2$ into $ g(x)=3x^{3}-5x^{2} $:
$$
\begin{align*}
g(-0.2)&=3\times(-0.2)^{3}-5\times(-0.2)^{2}\
&=3\times(-0.008)-5\times(0.04)\
&=- 0.024 - 0.2\
&=-0.224
\end{align*}
$$

## Step3: Calculate $ g(0.2) $
Substitute $ x = 0.2$ into $ g(x)=3x^{3}-5x^{2} $:
$$
\begin{align*}
g(0.2)&=3\times(0.2)^{3}-5\times(0.2)^{2}\
&=3\times(0.008)-5\times(0.04)\
&=0.024-0.2\
&=- 0.176
\end{align*}
$$

## Step4: Calculate the average rate of change
Using the formula $ \frac{g(b)-g(a)}{b - a} $ with $ a=-0.2$, $ b = 0.2$, $ g(a)=-0.224$ and $ g(b)=-0.176$:
$$
\begin{align*}
\frac{g(0.2)-g(-0.2)}{0.2-(-0.2)}&=\frac{-0.176-(-0.224)}{0.2 + 0.2}\
&=\frac{-0.176 + 0.224}{0.4}\
&=\frac{0.048}{0.4}\
&=- 0.2
\end{align*}
$$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for average rate of change

Step2: Calculate \( g(-0.2) \)

Step3: Calculate \( g(0.2) \)

Step4: Calculate the average rate of change

Answer: