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Geometric Definition of Derivative

Geometric Definition of Derivative
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2018-08-24 04:09
CalculusDerivativeGeometric Construction
This example demonstrates the geometric definition of the derivative, where the slope of the tangent line equals the derivative of the function at a point. Key mathematical concepts include the derivative, tangent line, and slope. The construction involves using GeoGebra commands like Point, Segment, Line, and Tangent to create the tangent line and calculate the slope. Suitable for high school students or college students learning calculus fundamentals.

GeoGebra Commands & Parameters

  1. Point(f) → A
  2. Segment(A, A_x) → g
  3. Segment(A, A_y) → i
  4. Segment(D, B) → d
  5. Segment(D, C) → e
  6. Line(A, D) → a
  7. Tangent(A, f) → b
  8. Intersect(b, xAxis) → E
  9. Intersect(a, xAxis) → F
  10. Angle(D, F, A_x) → β
  11. Angle(A_x, E, D) → α

AI Drawing Prompt Reference

Draw the graph of a function f, and at a point A, draw the tangent line b. Then draw two perpendicular lines from A to the x-axis, g and i. Next, draw a line segment from A to the intersection point E of the tangent line b and the x-axis. Draw a horizontal line a passing through A, and find the intersection point F of line a and the x-axis. Finally, measure the angles ∠DFA and ∠AED.
The prompt above was compiled from the original drawing commands and is for reference only.