Explore a Linear Piecewise Derivative

1 Explore

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?

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2 The Fine Print

**Requirements:**

These activities require web access using a browser that supports HTML5 and JavaScript. (That means almost any current browser.) No purchase is required, and there’s no advertising anywhere.

**Release Information**

Release: 2015Q4Update2, Semantic Version: 4.5.1-alpha, Build Number: 1026.6-wsp-widgets, Build Stamp: stek-macbook-pro/20180605163618

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“You may freely use Web Sketchpad in your own Web pages, provided you do so for non-commercial use only” [per kcpt.github.io].

License: Creative Commons CC-BY-NC-SA 4.0

**Update History:**

23 April 2018: Uploaded version 1 of this page.