Type any function into the input bar on the right of the applet ( f(x)=sin(x) is a useful example that has already been provided, but you may enter what you'd like).

Point A is a point on your function, and can be changed using the slider below the input box

Point B is a point on the derivative of your function, and will trace the movements of A.

Using the show f'(x) check box you can toggle the graph of the derivative on and off.

The value s shows you the slope of the tangent line of the function at any given point A

The play button will animate the slider, and show you how the points move together. Feel free to hit pause at any time.

Play with the applet above, and use your observations to answer the following questions:
1)The value s shows you the slope of the tangent line of the function at any given point A. How does this slope (s) relate to the location of point B?
2)Look at the position of point B when s is positive versus when s is negative. Do you see a pattern? What is it? (Hint: look at B's position with respect to the x axis)
3)Whenever B crosses the x axis something in particular happens to our original function. In mathematical terms, what could we call point A at any moment that point B is actually on the x axis? (Hint: Point A would be either a relative ___________ or a relative ___________ for our function, depending on if B crosses the x axis from positive to negative or from negative to positive.)