Concavity and Average Rate of Change
Choose any function you would like for .
Points are plotted that have -coordinates that are units apart. Then these points are connected with line segments.
This allows us to compare average rate of change on intervals of equal size (size ). We can look at the slopes of these segments to get an idea of where the average rate of change is increasing or decreasing.
When does it reach its maximum/minimum? This is called the inflection point. The smaller value we use for , the better we could approximate it, but it will be harder and harder to see the difference in slope for shorter and shorter segments.