Choose any function you would like for [math]f\left(x\right)[/math].[br][br]Drag point [math]P[/math] anywhere on the graph you would like and observe how the slope of the tangent line changes. This represents the [b]instantaneous rate of change[/b].[br][br]As we move the point we can see if this rate of change increasing or decreasing.[br][br]If the rate of change is [u]increasing[/u], the graph is [u]concave up[/u].[br][br]If the rate of change is [u]decreasing[/u], the graph is [u]concave down[/u].[br][br]When does the rate of change reach its maximum/minimum? This is called an [b]inflection point[/b].