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Activity:
Graphing f '(x): Increasing, Decreasing, Concavity |
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| Go to: |
http://www.teacherlink.org/.../home.htm
(opens a new window)
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| Description: |
This activity is designed to follow the activities From Secant Lines to Tangent Lines and Slopes and Derivatives [referenced below], but it can easily stand on its own. Using a dynamic tangent line and the value of the tangent line's slope, students analyze the graph of a function, investigating relationships between the function's first derivative, absolute and local extrema, intervals of increasing and decreasing, concavity, and inflection points. As the lesson progresses, students create and refine a sketch of f '(x). |
| Technology Type: |
Sketchpad | |
| Author: |
teacherlink.org--Center for Technology and Teacher Education |
| Language: |
English | |
| Cost: |
Does not require payment for use |
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| Courses: |
PreCalculus |
increasing, decreasing and constant rates of change, derivative, tangent line |
| Calculus |
Derivatives analytically, Derivative at a Point, Slope of a curve at a point, Tangent line, Graph of f vs. f', Meaning of the sign of f', Concavity and the sign of f", Points of inflection |
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