The problem asks for the average rate of change of the function $f(x)$ on the interval $6 \leq x \leq 7$.

The formula for the average rate of change of a function over an interval $[a, b]$ is:

$\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}$

Here, $a = 6$ and $b = 7$. To solve this, we need to determine the function values $f(6)$ and $f(7)$ from the graph.

• At $x = 6$, it looks like $f(6) = 0$ (the graph crosses the x-axis).
• At $x = 7$, it appears that $f(7) = 16$ (the graph rises to approximately 16).

Now, applying the formula:

$\text{Average rate of change} = \frac{f(7) - f(6)}{7 - 6} = \frac{16 - 0}{1} = 16$

Thus, the average rate of change is $16$.

Would you like more details or have further questions?

Here are some related questions you might explore:

1. What is the average rate of change between $x = 5$ and $x = 6$?
2. How do you interpret the slope of a function in terms of its graph?
3. What does it mean when the average rate of change is negative?
4. How does the shape of the graph influence the sign of the average rate of change?
5. Can you calculate the instantaneous rate of change at a specific point using this graph?

Tip: The average rate of change over an interval is similar to finding the slope of the secant line connecting two points on the function graph.