What does average rate of change mean?
Understand the Problem
The question is asking for the definition and explanation of the concept of 'average rate of change'. This concept is commonly used in mathematics and calculus to describe how a quantity changes on average over a certain interval.
Answer
A measure of how much the function changes per unit interval, on average, over a specific interval.
The average rate of change measures how much a function changes per unit interval, on average, over a specific interval. It is derived from the slope of the straight line connecting the interval's endpoints on the graph.
Answer for screen readers
The average rate of change measures how much a function changes per unit interval, on average, over a specific interval. It is derived from the slope of the straight line connecting the interval's endpoints on the graph.
More Information
The average rate of change is similar to the concept of slope in linear functions and can be calculated using the formula \( \frac{f(b) - f(a)}{b - a} \), where \( a \) and \( b \) are two points on the function \( f(x) \).
Sources
- Average Rate of Change - Definition, Formula, Examples - Cuemath - cuemath.com
- Average Rate Of Change Formula in Algebra (Solved Example) - byjus.com
- 1.3: The Average Rate of Change of a Function - math.libretexts.org
