Average rate of change

Definition

The average rate of change of a function between two points is the change in the function's value divided by the change in the input values. It represents the slope of the secant line connecting these points on the graph.

5 Must Know Facts For Your Next Test

1. The formula for average rate of change is $(f(b) - f(a)) / (b - a)$ where $a$ and $b$ are input values.
2. It can be interpreted as the slope of the secant line through points $(a, f(a))$ and $(b, f(b))$ on a graph.
3. It is used to measure how much a function changes on average between two specific input values.
4. Average rate of change can be positive, negative, or zero depending on whether the function is increasing, decreasing, or constant over the interval.
5. It provides an overall view of how a function behaves between two points but does not give information about behavior at individual points within that interval.

Review Questions

• What is the formula for calculating the average rate of change of a function?
• How do you interpret a negative average rate of change?
• If $f(x)$ represents a linear function, what will be its average rate of change over any interval?

Related terms

Instantaneous Rate Of Change: The derivative of a function at a particular point; it represents how fast the function's value is changing at that specific point.

Secant Line: A line that intersects two or more points on a curve. The slope of this line gives us the average rate of change over an interval.

Slope: $m = (y_2 - y_1) / (x_2 - x_1)$; it measures how steep a line is and can be used to describe linear functions or secant lines.