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Curves and Stationary Points

Curves and Stationary Points
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2019-12-04 17:52
FunctionCalculusDerivativeOptimization
This example demonstrates how to analyze the shape of function curves and locate their stationary points using GeoGebra. Key math concepts include derivatives, function extrema, and analytical geometry. It leverages commands like Intersect, FractionText, If, and Segment, along with objects such as segments and points, to construct the visualization. Ideal for high school and above students studying calculus, function analysis, and mathematical modeling.

GeoGebra Commands & Parameters

  1. Intersect(f', xAxis) → A, B, C
  2. Intersect(f'', xAxis) → D, E
  3. FractionText(a) → fa
  4. FractionText(b) → fb
  5. FractionText(c) → fc
  6. FractionText(d) → fd
  7. FractionText(e) → fe
  8. FractionText((a * 4)) → ffa
  9. FractionText((3 * b)) → ffb
  10. FractionText((2 * c)) → ffc
  11. FractionText(d) → ffd
  12. FractionText(((4 * 3) * a)) → fffa
  13. FractionText(((3 * 2) * b)) → fffb
  14. FractionText((2 * c)) → fffc
  15. If(Defined[SP1], If[Defined[SP2], If[Defined[SP3], 3, 2], 1], 0) → sps
  16. If(Defined[PI1], If[Defined[PI2], 2, 1], 0) → pis
  17. Segment(SP1, A) → f_1
  18. Segment(SP2, B) → g_{2}
  19. Segment(SP3, C) → g_1
  20. Segment(PI1, D) → h_1
  21. Segment(PI2, E) → i_1