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Activity: Graphing f '(x): Increasing, Decreasing, Concavity
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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: 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