This applet allows students to sketch the derivative of a function with almost immediate feedback and develop their understanding of the derivative in relationship to the original function. It enables students to see the role that inflection points play in the process.

Type of Material:

Java applet

Recommended Uses:

Classroom demonstration; student exploration or enrichment

Technical Requirements:

Java-enabled browser; JAVA 2 plug-in

Identify Major Learning Goals:

Develop a geometrical understanding of the derivative of a function through repeated creation of real-time visual examples.

Target Student Population:

Beginning Calculus students

Prerequisite Knowledge or Skills:

Graphing skills, familiarity with the concept of derivative

Content Quality

Rating:

Strengths:

The applet requires students to connect the concept of slope of the tangent line to the actual graph of a function. Students can develop their geometrical understanding of the derivative by practicing with the applet. The role of inflection points becomes clear in the process as do the zero slope values at relative minima and maxima. The author is commended for this innovative application of technology.

Concerns:

There was one case in which the value of the derivative did not correspond with the graph (a straight line with an approximate slope of 1 was shown to have a constant derivative with an approximate value of 1.8). In the linked example concerning the use of a T-table, it is not clear how some of the non-zero values in the T-table are calculated. For example, how does the author obtain an approximate slope of -0.2 at x = -5? Also, several of the points from the T-table are obviously plotted incorrectly in the graph at the bottom of the page: x = -5, -2, -1 and 0.
Understanding would be enhanced if the tangent line was also visible its not visually obvious what the derivative graph is displaying.

Potential Effectiveness as a Teaching Tool

Rating:

Strengths:

This applet provides excellent visual practice in drawing derivatives based on a given function. It takes a bit of practice and concentration to catch onto the process, but the almost immediate feedback is most helpful. The linked example with the T-table is also helpful.

Concerns:

While there is a linked example of how to carry out the derivative construction process via the use of a T-table, more information concerning the facts that the derivative is 0 at the functions relative extrema and that the derivative has its own relative extrema at the functions inflection points would have been helpful. The user will presumably sketch the derivative without the use of a T-table. A couple of similar examples with simpler curves would be useful.
Understanding would be enhanced if the tangent line was also visible its not visually obvious what the derivative graph is displaying.

Ease of Use for Both Students and Faculty

Rating:

Strengths:

No technical difficulties were encountered in the use of this site.

Concerns:

In one case where the original graph did not appear to begin at the left edge of the applet window, it wasnt evident that the user had to begin dragging the mouse from the left edge of the window. The natural tendency in these cases is to begin dragging the mouse at the point where the graph appears to begin; however, this doesnt activate the derivate plot. This could be addressed by modifying Instruction #1 to indicate the need to begin dragging the mouse at the left edge of the applet window or by eliminating functions that do not appear to begin at the left edge of the applet window.
The instruction drag the mouse could be misinterpreted as rollover. In fact it means click and hold as you drag. It is not clear what information is given by the graph of the mouse trace no matter the y value of the mouse, the derivative graph is the same because it illustrates the provided sample graph not the graph of the mouse

Creative Commons:

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