The average rate of change of a function $b(x)$ over an interval $[x_1, x_2]$ is given by:

$\frac{b(x_2) - b(x_1)}{x_2 - x_1}$

In this case, we want to find the average rate of change of $b(x)$ over the interval $[-2, 4]$.

Using the values provided:

• $x_1 = -2$ and $b(x_1) = -5$
• $x_2 = 4$ and $b(x_2) = 5$

Substitute these values into the formula:

$\frac{b(4) - b(-2)}{4 - (-2)} = \frac{5 - (-5)}{4 + 2} = \frac{5 + 5}{6} = \frac{10}{6} = \frac{5}{3}$

So, the average rate of change of $b(x)$ over the interval $[-2, 4]$ is $\frac{5}{3}$.

Would you like a breakdown of each calculation step?

Here are five related questions to expand your understanding:

1. How is the average rate of change different from the instantaneous rate of change?
2. What is the significance of positive, negative, and zero rates of change?
3. How can you determine if a function is increasing or decreasing over a given interval?
4. How would you interpret the rate of change if it were negative?
5. How does the interval size affect the average rate of change?

Tip: For linear functions, the average rate of change over any interval is constant and equals the slope of the line.