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Derivative vs Tangent Slope

Derivative vs Tangent Slope
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2020-04-25 15:56
VectorFunctionCoordinate GeometryCalculusDerivative
This example demonstrates the relationship between the derivative value of a function and the slope of its tangent line. It involves core math concepts like derivatives, tangent functions, polynomial functions, vectors, and calculus. Construction highlights include using GeoGebra commands/objects such as Point, Tangent, Circle, Intersect, Segment, Slope, Vector, Translate, and Midpoint. Suitable for high school and above students learning calculus and analytical geometry.

GeoGebra Commands & Parameters

  1. Textfield(f) → ChampTexte1
  2. Point(f) → M
  3. Tangent(M, f) → g
  4. Circle(M, 6) → c
  5. Intersect(c, g) → B, C
  6. Segment(C, B) → h
  7. Slope(g) → a
  8. Vector(D, E) → u
  9. Vector(D, F) → v
  10. Translate(E, Vector[(If[b < 5, b / 5, 1] * v)]) → E'
  11. Translate(D, Vector[(If[b < 5, b / 5, 1] * v)]) → D'
  12. Vector(D', E') → w
  13. Segment(M, F) → i
  14. Segment(G, H) → j
  15. Segment(I, J) → k
  16. Segment(K, L) → l
  17. Midpoint(E', D') → A
  18. Midpoint(M, D) → N
  19. Midpoint(M, D) → O
  20. Midpoint(M, D) → P
  21. Translate(M, Vector[(If[b < 5, b / 5, 1] * v)]) → M'

AI Drawing Prompt Reference

Draw a function graph and mark a point on it. Then, sketch the tangent line at that point and the circle centered at the point with radius 6. Connect the intersection points of the circle and the tangent line. Display the slope of the tangent line, and create two vectors based on it. Use vector operations to obtain new points and connect them with line segments. Finally, calculate the midpoints of several points and connect them to show the relationship between the derivative of the function and the slope of its tangent line.
The prompt above was compiled from the original drawing commands and is for reference only.