To find the average rate of change of $g(x)$ from $x = 0$ to $x = 6$, we use the formula for the average rate of change:

$\text{Average rate of change} = \frac{g(x_2) - g(x_1)}{x_2 - x_1}$

Given:

• $x_1 = 0$, $g(0) = 2$
• $x_2 = 6$, $g(6) = 4$

Now, substitute the values into the formula:

$\text{Average rate of change} = \frac{g(6) - g(0)}{6 - 0} = \frac{4 - 2}{6} = \frac{2}{6} = \frac{1}{3}$

Thus, the average rate of change of $g(x)$ from $x = 0$ to $x = 6$ is $\frac{1}{3}$.

Would you like further details or clarifications?

Here are 5 related questions for deeper exploration:

1. What is the rate of change of $g(x)$ from $x = 2$ to $x = 8$?
2. How would you interpret a negative average rate of change?
3. How does the rate of change affect the shape of the graph of $g(x)$?
4. What is the average rate of change of $f(x)$ from $x = 0$ to $x = 9$?
5. How can you find the instantaneous rate of change of $g(x)$ at $x = 4$?

Tip: The average rate of change between two points can be thought of as the slope of the line connecting those points on a graph.