Concavity

When you first load the app, it shows you the function . What is average rate of change in this function from to ? What is the average rate of change from to ?

As you move from left to right, is the average rate of change of the function increasing or decreasing? Does the secant line get steeper or less steep?

A function is said to be concave up if the average rate of change increases as you move from left to right, and concave down if the average rate of change decreases. Is concave up or concave down?

Play around with each of the other functions. Which ones are concave up? Which ones are concave down?

Some functions switch back and forth so that they're concave down in some places and concave up in others. Are there any functions like this in the app above? If yes, which ones have this property and where do they switch from being concave down to concave up or visa versa?