Kyle Derivative Applet

Kyle King
The applet gives students the opportunity to explore a variety of functions and derivatives with their graphs.
Point B has coordinates (x,y). What determines those coordinates? Why is the graph of g(x) a horizontal line when f(x) is a linear function (such as f(x)=3x +2 or -4x-5)? Could you predict where the graph of g(x) will touch the x-axis by just examining the graph of f(x)?