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Implicit Differentiation: Intro

In the applet below, note the graph of the equation . Please don't tamper with slider, input box, or checkbox quite yet. Yet do so when prompted to by the questions below the applet.


Warm Up: Given the equation , use any one (or more) of the techniques of differentiation you've learned thus far to determine when .


Click on the "Show Derivative at This Input Value" checkbox to check your work. Does what you see surprise you? Why does this (the fact that there are 2 possible values for ) occur?

Feel free to drag either of the gray points around. You can also change the radius of the circle as well.