Concavity and Tangent Lines
Choose any function you would like for .
Drag point anywhere on the graph you would like and observe how the slope of the tangent line changes. This represents the instantaneous rate of change.
As we move the point we can see if this rate of change increasing or decreasing.
If the rate of change is increasing, the graph is concave up.
If the rate of change is decreasing, the graph is concave down.
When does the rate of change reach its maximum/minimum? This is called an inflection point.