Although, strictly speaking, this is not about physics, it should be useful to physics teachers when they teach their students on how to obtain the shape of the acceleration-time graph from a velocity-time graph.

I saw this self-running animation ([url=http://www.math.umn.edu/~garrett/qy/TraceTangent.html]http://www.math.umn.edu/~garrett/qy/TraceTangent.html[/url]) and was wondering if Prof Hwang could improve the applet and share with physics teachers.

[b]1st improvement:[/b] user can move the pointer along the given curve to see how the tangent changes and the value of the tangent's gradient is being displayed above the line as the point is being moved.

[b]2nd improvement:[/b] A second graph to be displayed vertically below the given graph to show the variation of the tangent's gradient (first derivative) accordingly.

[b]3rd improvement:[/b] the user can decide on the original graph (say, by inputting an equation, or by selecting from a few "standard" graphs)

Thank you.