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To find the average rate of change of the function \( f \) on the interval \([10, 60]\), we can use the formula for the average rate of change, which is:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

Here, \(a = 10\) and \(b = 60\).

From the graph:

- At \(x = 10\), the value of \(f(10)\) appears to be approximately \(f(10) = 200\).
- At \(x = 60\), the value of \(f(60)\) appears to be approximately \(f(60) = 800\).

Now, applying the formula:

\[
\text{Average Rate of Change} = \frac{f(60) - f(10)}{60 - 10} = \frac{800 - 200}{60 - 10} = \frac{600}{50} = 12
\]

So, the average rate of change of the function \( f \) on the interval \([10, 60]\) is \( 12 \).

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Do you have any further questions or would you like more details?

Here are some related questions you might explore:
1. How do you interpret the average rate of change in a real-world context?
2. What is the significance of a positive or negative average rate of change?
3. Can the average rate of change be zero? If so, under what circumstances?
4. How can the average rate of change be used to approximate instantaneous rates of change?
5. How do you calculate the instantaneous rate of change using limits?

**Tip:** The average rate of change of a function over an interval is similar to the slope of the line connecting the endpoints of the graph on that interval.

Find the average rate of change of the function f on the interval [10, 60].

Learn how to find the average rate of change of a function on a given interval [10, 60] using the formula (f(b) - f(a)) / (b - a). Understand how to interpret the graph to identify the values and apply the formula for accurate results. Suitable for students in Grades 9-11.

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