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Change of Sign: Decimal Search

Change of Sign: Decimal Search
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2014-06-18 16:03
FunctionCalculusDerivativeOptimizationGraphing
In collections A Level: Numerical Methods for Solving Equations
This example demonstrates the Decimal Search method for identifying the existence of roots in a continuous function. It involves core mathematical concepts like the Intermediate Value Theorem, interval bisection, and confidence intervals for roots. GeoGebra commands used include Intersect, Element, Textfield, If, Segment, and TableText for constructing the visualization. Suitable for high school students studying numerical methods, particularly for MEI C3 coursework.

GeoGebra Commands & Parameters

  1. Intersect(f, g) → x_0, x_1, x_2, x_3
  2. Element(rootlist, rootnumber) → root
  3. Textfield(f) → inputBox1
  4. Element(xmaxlist, zoomnumber) → xmax
  5. Element(xminlist, zoomnumber) → xmin
  6. Element(yzoomadjustlist, zoomnumber) → yzoomadjust
  7. If(level2increment < 1, clevervalue, intsrch) → startsearchvalue
  8. Segment((A13, 0), (A13, B13)) → C13
  9. Segment((A13, 0), (A13, B13)) → D13
  10. Segment((A14, 0), (A14, B14)) → C14
  11. Segment((A15, 0), (A15, B15)) → C15
  12. Segment((A16, 0), (A16, B16)) → C16
  13. Segment((A17, 0), (A17, B17)) → C17
  14. Segment((A18, 0), (A18, B18)) → C18
  15. Segment((A19, 0), (A19, B19)) → C19
  16. Segment((A20, 0), (A20, B20)) → C20
  17. Segment((A21, 0), (A21, B21)) → C21
  18. Segment((A22, 0), (A22, B22)) → C22
  19. Segment((A23, 0), (A23, B23)) → C23
  20. Segment((A14, 0), (A14, B14)) → D14
  21. Segment((A15, 0), (A15, B15)) → D15
  22. Segment((A16, 0), (A16, B16)) → D16
  23. Segment((A17, 0), (A17, B17)) → D17
  24. Segment((A18, 0), (A18, B18)) → D18
  25. Segment((A19, 0), (A19, B19)) → D19
  26. Segment((A20, 0), (A20, B20)) → D20
  27. Segment((A21, 0), (A21, B21)) → D21
  28. Segment((A22, 0), (A22, B22)) → D22
  29. Segment((A23, 0), (A23, B23)) → D23
  30. TableText(matrix1, "cc") → text3

AI Drawing Prompt Reference

Draw the graph of a continuous function and use the decimal search method to find its roots. First, mark several intervals on the x-axis and represent the search process in each interval with vertical line segments from the x-axis to the function graph. Then, label the midpoints of each interval with colored line segments and indicate the roots of the function. Finally, add text annotations next to the graph to explain the steps and principles of the decimal search method, including the Intermediate Value Theorem and interval bisection.
The prompt above was compiled from the original drawing commands and is for reference only.