Tangent Line Surfer

Please be patient while the Java applet loads.

Directions: Move point x along the x-axis to move point P and its tangent line. Turn on "Trace" in lower-right to trace the derivative of f (slope values). Different functions can be "surfed" by clicking on the buttons below the sketch.

When the slope of the tangent line is negative:
The function is doing what?
Where is the derivative tracing?

When the slope of the tangent line is positive:
The function is doing what?
Where is the derivative tracing?

When the tangent line is horizontal:
What do you notice about the function?
Where is the derivative tracing?