This applet is part of a collection of Java Applets that can be used in the teaching and learning of undergraduate Calculus. This particular applet allows the user to explore the relationship between the slopes of secant lines and the slope of the tangent line to a user-defined graph at a user-specified point. Please see the reviews of the following related sites:

To understand how the limit process is used to define the slope of the tangent line to a given graph at a specified point.

Target Student Population:

Students in Calculus I course or a Survey of Calculus course

Prerequisite Knowledge or Skills:

The definition of limit.

Content Quality

Rating:

Strengths:

This applet allows the user to specify a function, f , a point, (x,f(x)), at which to graph a tangent line, and a point, (x + h,f(x + h)), to use as the second point for defining the secant line. The user is then able to click on the graph to make h smaller and smaller while examining its effect on the slope of the secant line as compared to the displayed value of the slope of the tangent line. A zoom feature of the applet allows user to run the simulation for very small values of h, and effectively use the applet to illustrate the geometric interpretation and the definition of the derivative of a function.

Concerns:

The Web page containing the applet could use an introduction section targeting potential Calculus students who plan to use the applet.

Potential Effectiveness as a Teaching Tool

Rating:

Strengths:

This applet allows the user to explore the definition of the slope of the tangent line both graphically and numerically. Because the user may choose any function and starting point, it is easy to choose very meaningful examples. It also can be used to graphically illustrate linear approximations of functions at a given point.

Concerns:

This applet could be easily related to some major Calculus topics such as limits and derivative of the function. Emphasizing this connection would certainly make it a better educational module. A couple of textbook examples would be a plus

Ease of Use for Both Students and Faculty

Rating:

Strengths:

This applet has clearly marked buttons. They allow the user to enter functions, view graph range controls, view slope information, and view accurate cursor location information. The function syntax is similar to most graphing calculators, and is clearly explained on a separate page. There are also 11 commonly used functions available, including sine, cosine, tangent, arcsine, arctangent, exp, and absolute value. The use of the applet is fairly intuitive. The average user can begin using it immediately with a brief introduction. Although this applet is copyrighted,
it is available for free academic, non-profit use. The class files and most of the source code is also made available for download.

Concerns:

It is necessary to explain how to use each applet. It would be nice if more explicit instructions were given on each function. For instance, it is not clear how one changes the graphing window and it seems to draw the intersection of the axes at the center of the drawing canvas rather than at (0,0). A simple way to print different plots might be useful. The site could use some navigation buttons.

Creative Commons:

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