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Definition of Derivative

Definition of Derivative
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2019-11-03 21:01
FunctionCalculusDerivative
This example illustrates the definition of a derivative. Using GeoGebra, users can visually understand the concept of a derivative. Key mathematical concepts include derivatives, tangents, and slopes. The construction summary mentions the use of commands like Tangent, Line, and Slope. Suitable for high school mathematics education and learning derivative concepts.

GeoGebra Commands & Parameters

  1. Tangent(A, f) → g
  2. Line(A, B) → h
  3. Slope(h) → a
  4. Slope(g) → c
  5. Textfield(f) → InputBox1
  6. OrthogonalLine(A, tmp1) → i
  7. Intersect(i, tmp1) → C
  8. Segment(C, A) → j
  9. OrthogonalLine(B, tmp1) → k
  10. Intersect(tmp1, k) → D
  11. Segment(D, B) → l
  12. Segment((b, 0), B) → n
  13. Segment((xcur, 0), A) → p
  14. Intersect(n, g) → E
  15. Segment(E, (0, y(E))) → q
  16. Segment(C, (0, y(E))) → r
  17. Segment((x(D) + 0.1, y(D)), (x(C) + 0.1, y(C))) → m

AI Drawing Prompt Reference

Draw a function f(x) and select two points A and B on it. Draw the tangent line at point A and the secant line through points A and B. Calculate and display the slopes of these lines. Draw lines perpendicular to the tangent and secant, and find their intersections with the function. Connect these intersections to the origin to form a triangle. Finally, draw a perpendicular line segment from point B to the tangent line.
The prompt above was compiled from the original drawing commands and is for reference only.