In this activity, you can adjust the linear pieces shown on the left. Arrange these pieces to approximate a conjectured derivative graph. (Make sure the points are in left-to-right order when you finish adjusting.)
When you finish arranging your approximately-conjectured derivative, press Reveal to show a function matching the derivative you've specified.
Page 1: What's the shape of a velocity graph when a tennis ball is dropped from a height and bounces off the floor? Use this page to create a conjecture of the shape of the velocity graph, and then use Reveal Function to check your conjecture. Press Reveal Function again to hide the position graph while you're adjusting your conjecture.
Page 2: Use this page to create a piecewise linear derivative function for another scenario (for instance, the height of water in an interestingly-shaped container being filled at a constant rate). How does the shape of the bottle determine the derivative of the function that describes the height of the water relative to the amount of water poured in?
2 The Fine Print