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Graphing the Derivative of a Function

Graphing the Derivative of a Function
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2019-07-03 19:55
FunctionCalculusDerivativeGeometric ConstructionGraphing
This example demonstrates how to graph the derivative of a function by dynamically plotting the slope of tangents, illustrating the relationship between the derivative and the original function's graph. Core mathematical concepts include the geometric meaning of derivatives and the local properties of function graphs. Key GeoGebra commands and objects used in the construction are Point, Tangent, Circle, Intersect, Segment, Vector, and Textfield, which calculate tangent slopes and plot their trajectories to form the derivative graph. Suitable for high school and above students learning calculus concepts.

GeoGebra Commands & Parameters

  1. Point(f) → A
  2. Tangent(A, f) → c
  3. Circle(A, 1.5) → d
  4. Intersect(d, c, 1) → C
  5. Intersect(d, c, 2) → D
  6. Segment(C, D) → e
  7. Vector(A, D) → u
  8. Vector(A, C) → v
  9. Textfield(f) → InputBox1

AI Drawing Prompt Reference

Draw a function graph and dynamically show its derivative. First, plot the function curve, then select a point on the curve and draw the tangent line at that point. Draw a circle centered at this point, and find the intersections of the circle with the tangent line. Connect these intersection points to form a segment. Draw vectors from the center of the circle to each intersection point, and the trajectory of these vectors represents the derivative graph. Also, label the original function expression.
The prompt above was compiled from the original drawing commands and is for reference only.