What is the average rate of change of f(x) over the interval [2,5]?

The **average rate of change** of a function \( f(x) \) over an interval \([a, b]\) is given by the formula:

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

In your case, the interval is \([2, 5]\). So, we need to compute:

\[
\text{Average rate of change} = \frac{f(5) - f(2)}{5 - 2} = \frac{f(5) - f(2)}{3}
\]

To find the specific average rate of change, you'll need to know the values of \( f(2) \) and \( f(5) \). 

Do you have those values, or do you know the function \( f(x) \)?

Would you like details or have any questions on this? 

Here are 5 related questions you might consider:
1. What is the formula for the function \( f(x) \)?
2. How does the average rate of change relate to the derivative?
3. Can you explain how to calculate instantaneous rates of change?
4. What happens to the rate of change when the interval becomes very small?
5. How would the average rate of change differ for a linear versus a quadratic function?

**Tip:** The average rate of change is equivalent to the slope of the secant line between the points \( (a, f(a)) \) and \( (b, f(b)) \) on the graph of \( f(x) \).

Discover how to calculate the average rate of change of a function f(x) over the interval [2,5] using the formula (f(b) - f(a)) / (b - a). This concept is foundational in calculus, covering secant lines and rates of change, ideal for students in Grades 10-12.

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