This site contains an interactive applet that illustrates the concept of implicit differentiation. By changing a set of parameters the user can generate a family of equations whose graphs are rendered. Then the tool draws the tangent line at the point and finds its slope.
Type of Material:
Simulation
Recommended Uses:
This site can be used for an in-class demonstration, self-study, or group activity
Technical Requirements:
Any browser.
Identify Major Learning Goals:
To explore and develop a better understanding of implicit differentiation.
Target Student Population:
Calculus I Students.
Prerequisite Knowledge or Skills:
First semester of Calculus.
Content Quality
Rating:
Strengths:
This site allows users to explore and visualize the concept of implicit differentiation that is typically introduced in the first semester of Calculus. The user has control (via sliders) over 3 parameters. By changing these parameters, it is possible to generate a variety of equations that implicitly define curves in xy-plane. Then the user can click and drag a point on the curve with the tangent line shown and slope calculated numerically. Several questions are also provided to guide the exploration.
Concerns:
None.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The site can be used as a part of in-class demonstration, self-guided activity, or a hands-on group activity. Instructors could easily add to the exploratory questions.
Concerns:
None.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
This applet is very easy to use. The graph is clean and easy to work with.
Concerns:
None.
Creative Commons:
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