Yes, in AP Calculus, the average rate of change between two points is essentially the slope of the line connecting those two points. The formula for the average rate of change is:

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

Where:

• $f(a)$ and $f(b)$ are the function values at the points $a$ and $b$,
• $a$ and $b$ are the x-coordinates of the points.

This is the same as calculating the slope of the secant line passing through the points $(a, f(a))$ and $(b, f(b))$.

Example:

If you have the points $(a, f(a))$ and $(b, f(b))$, then the slope (or average rate of change) would be:

$\text{Slope} = \frac{f(b) - f(a)}{b - a}$

This formula gives the rate at which the function is changing on average between these two points, not the instantaneous rate of change, which is what you find using derivatives.

Would you like to see an example in action, or do you have further questions on this?

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Related Questions:

1. How does the instantaneous rate of change differ from the average rate of change?
2. What is the slope of a secant line, and how does it relate to the average rate of change?
3. How do we find the average rate of change from a graph of a function?
4. Can the average rate of change be negative? What does it mean geometrically?
5. How does the average rate of change relate to the concept of limits?

Tip: When calculating the average rate of change, always remember to check the units of the function values and the interval to ensure your result makes sense in context!