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Exercise 3 - Rate of Change

Exercise 3 - Rate of Change
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2017-12-04 17:01
FunctionCalculusDerivative
This example demonstrates the concept of the rate of change, specifically the derivative, by randomly generating functions and allowing users to observe the slope changes at different points. Key mathematical concepts include derivatives and slopes. It utilizes commands such as Random, RandomElement, Textfield, Polygon, LaTeX, Vector, OrthogonalLine, Point, etc., in GeoGebra. Suitable for high school mathematics education and learning the concept of derivatives.

GeoGebra Commands & Parameters

  1. Random(1, 5) → deltax
  2. RandomElement({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}) → c
  3. Textfield(h) → InputBox1
  4. RandomElement({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}) → a_1
  5. Random(-10, 10) → b_1
  6. RandomElement({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}) → c_1
  7. Random(-10, 10) → d_1
  8. Textfield(m) → InputBox2
  9. Textfield(g) → InputBox3
  10. Textfield(f) → InputBox4
  11. Polygon(B, C, D, E) → poly1, b_2, c_1, d_2, e_1
  12. LaTeX(a, true, true) → text10
  13. LaTeX(b, true, true) → text11
  14. Random(1, 10) → nRand
  15. Textfield(stepx) → InputBox5
  16. Vector(A, F) → u
  17. OrthogonalLine(F, u) → q
  18. Point(q) → G
  19. Vector(F, G) → v
  20. TableText({{A1_1, B_1}, {A6, B6}, {A7, B7}, {A8, B8}, {A9, B9}, {A10, B10}}, "|_r") → text1

AI Drawing Prompt Reference

Draw a graph of a randomly generated function and select a random point on the graph to draw the tangent line at that point. Create an input box for users to input the coefficients of the function, and dynamically adjust the function graph based on the input. Also, show the changes in the derivative and slope.
The prompt above was compiled from the original drawing commands and is for reference only.