Tangent to a curve

[tanghb]

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 (http://www.math.umn.edu/~garrett/qy/TraceTangent.html) and was wondering if Prof Hwang could improve the applet and share with physics teachers.

1st improvement: 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.

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

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

Thank you.

[Fu-Kwun Hwang]

I hope the following applet is what you need.

Put one diagram on top of another does not look good, so I re-arrange it to left/right style.

You can drag the point in the f(x) diagram to change x when the simulated is in paused state.
You can drag the slider at right hand side to change y-scale.
More suggestions are highly welcomed! To make it better. :-)

Embed a running copy of this simulation
<applet code='users.ntnu.fkh.tangentoffunction_pkg.tangentoffunctionApplet.class' archive='http://www.phy.ntnu.edu.tw/ntnujava/ejsuser/2/ejs_tangentoffunction.jar' name='tangentoffunction4992' id='tangentoffunction4992' width='817' height='643' mayscript=true><param name='draggable' value='true'></applet>
Embed a running copy link(show simulation in a popuped window)
<a href='http://www.phy.ntnu.edu.tw/ntnujava/msg.php?smfejs=4992' target='smfejs'>Run simulation</a>

Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop. This work is licensed under a Creative Commons Attribution 2.5 Taiwan License

• Please feel free to post your ideas about how to use the simulation for better teaching and learning.
• Post questions to be asked to help students to think, to explore.
• Upload worksheets as attached files to share with more users.

Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!

[tanghb]

Wow! Yes, that's what wished, and now I have got it. Thank you so much for helping!

I wonder if it is possible for user to choose to show only the graph of first derivative or the second derivative, or both. If not, it would be good just to indicate in words somewhere that the white line is the the graph of first derivative, and the red is for the second derivative. As teachers, we could see easily that the colors of the lines are already an indication of this, but many students may not be able to see this.

Once more suggestion: white line and gray background do not give sufficient contrast, especially when the applet is projected onto a screen in a classroom during the day. A black line should be better (then the color of the dot moving on the blue curve should be changed accordingly).

Thanks again!

[Fu-Kwun Hwang]

As you wish:
1. User can select check boxes to choose to show only the graph of first derivative or the second derivative, or both.
2. The color of white line has been changed to black line.


I would like to ask student to answer which curve is the derivate of the f(x) and tell me why/how s/he find out.
So I did not add those information in the diagram.

[tanghb]

That's great!

But just one more lttile suggestion: when only the graph of the first derivative is displayed, could the red tangent line on it be removed? i.e. only the moving dot along the graph should be shown. Of course, when the graphs of both the first and second derivatives are displayed, we need to show the moving red tangent line.

Thanks a lot again!

[Fu-Kwun Hwang]

If only right diagram is shown, the tangent line will be shown.
However, if both diagram are shown and second derivate are not shown, the tangent line will not be shown.

[tanghb]

Thanks for making the final modification. This will be a very useful simulation.