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Function Linearization Illustrator (Calculus)

Function Linearization Illustrator (Calculus)
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2016-11-02 17:45
FunctionCalculusDerivativeGeometric Construction
This dynamic and interactive GeoGebra example demonstrates the linearization of a function at a point, visually illustrating the approximation of the function by its tangent line. Key math concepts include derivatives, tangent lines, difference and slope, and linear approximation. Constructed using GeoGebra commands like Textfield, Tangent, Slope, Intersect, Segment, Polygon, with interactive elements such as InputBoxes and buttons. Ideal for university calculus instruction or self-study to understand local linearization properties.

GeoGebra Commands & Parameters

  1. Textfield(f) → InputBox9
  2. Textfield(g) → InputBox10
  3. Textfield(h) → InputBox11
  4. Textfield(k) → InputBox7
  5. Textfield(e) → InputBox1
  6. Textfield(i) → InputBox2
  7. Textfield(j) → InputBox3
  8. Textfield(l) → InputBox4
  9. Textfield(a) → InputBox5
  10. Tangent(A, f) → b
  11. Slope(b) → m_1
  12. Textfield(c) → InputBox6
  13. Textfield(d) → InputBox8
  14. Intersect(b, f_1) → L
  15. Intersect(f, f_1, 1) → D
  16. Segment(A, B) → g_1
  17. Segment(B, L) → dy
  18. Polygon(A, B, L) → poly1, l_1, a_1, b_1
  19. Segment(L, D) → h_1
  20. Textfield(dx) → InputBox12
  21. Textfield(f) → InputBox13