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Mapping Diagram of Derivatives

Mapping Diagram of Derivatives
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2018-05-20 19:30
FunctionCalculusDerivative
This example demonstrates the mapping diagram of derivatives, focusing on the core concept of derivatives. Using GeoGebra commands such as SelectedElement, Point, and Sequence, a clear mapping diagram of derivatives is constructed. Suitable for high school mathematics education, it helps students understand the geometric meaning of derivatives.

GeoGebra Commands & Parameters

  1. SelectedElement(L_4) → f
  2. Point(yAxis) → A
  3. Sequence((a, y(A)), a, -10, 10, 0.05) → L_1
  4. Sequence((f(a), 0), a, -10, 10, 0.05) → L_2
  5. Sequence(Segment[(a, y(A)), (f(a), 0)], a, -10, 10, 0.05) → L_3

AI Drawing Prompt Reference

Create a mapping diagram for derivatives. Draw a function curve on a coordinate plane, and place a reference point on the y-axis. Then, generate a series of x-coordinates from -10 to 10 with a step of 0.05)Skip, and for each x, find the corresponding y-value on the curve. Next, mark points on the x-axis with the same x-coordinates and y=0. Finally, draw line segments from each x-axis point to its corresponding curve point, illustrating the mapping from the x-axis to the curve and showing how the derivative changes.
The prompt above was compiled from the original drawing commands and is for reference only.