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Derivatives as Limits

Derivatives as Limits
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2018-07-15 18:34
FunctionDerivativeLimit
In collections Derivatives
This example illustrates the concept of derivatives as limits. By adjusting function f(x), observe how its derivative value at a point approximates through the limit process. Commands used include OrthogonalLine, Intersect, Segment, Derivative, and Textfield. Suitable for high school math education to help students understand the definition of derivatives.

GeoGebra Commands & Parameters

  1. OrthogonalLine(B, xAxis) → g
  2. Intersect(g, xAxis) → C
  3. Segment(B, C) → i
  4. Derivative(f) → f'
  5. Textfield(f) → InputBox1
  6. Intersect(xAxis, yAxis) → A
  7. Segment(A, C) → j

AI Drawing Prompt Reference

Draw a function graph and its derivative. Mark the origin on the x-axis, draw a vertical line from the origin to a point on the function graph, and connect this point to the intersection of the vertical line with the x-axis to form a segment. Select a point on the function graph, draw the tangent line at that point, and display its equation. Draw a horizontal segment between the origin and the tangent line to illustrate the concept of the derivative.
The prompt above was compiled from the original drawing commands and is for reference only.