In the applet below, note the graph of the equation [math]x^2+y^2=25[/math]. [br][br]Please don't tamper with slider, input box, or checkbox quite yet. Yet do so when prompted to by the questions below the applet.
[color=#980000][b]Warm Up: [/b][/color][br][br]Given the equation [math]x^2+y^2=25[/math], use any one (or more) of the techniques of differentiation you've learned thus far to determine [math]\frac{dy}{dx}[/math] when [math]x=3[/math].
Click on the "Show Derivative at This Input Value" checkbox to check your work. [br]Does what you see surprise you? [br][br]Why does this (the fact that there are 2 possible values for [math]\frac{dy}{dx}[/math]) occur?
Feel free to drag either of the gray points around. You can also change the radius of the circle as well.