Concavity and Average Rate of Change

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

Information: Concavity and Average Rate of Change