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Geogebra Calculus & Optimization Demo

Geogebra Calculus & Optimization Demo
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2022-08-21 16:20
PolygonFunctionCalculusDerivativeOptimization
This example dynamically demonstrates calculus optimization problems using GeoGebra, integrating function graphs, derivatives, and polygon constructions. Core concepts include derivatives, optimization, polygon construction, and function graphing. It utilizes commands like Polygon, CurveCartesian, Textfield, Sequence, Derivative, Sum, Centroid, and LaTeX. Suitable for high school and above students studying calculus, coordinate geometry, and optimization.

GeoGebra Commands & Parameters

  1. Polygon(A1, A2, A3, A4) → P1, a1, a2, a3, a4
  2. CurveCartesian((t * x(A2)) + ((1 - t) * x(A1)), (t * y(A2)) + ((1 - t) * y(A1)), t, 0, 1) → c1
  3. CurveCartesian((t * x(A3)) + ((1 - t) * x(A2)), (t * y(A3)) + ((1 - t) * y(A2)), t, 0, 1) → c2
  4. CurveCartesian((t * x(A4)) + ((1 - t) * x(A3)), (t * y(A4)) + ((1 - t) * y(A3)), t, 0, 1) → c3
  5. CurveCartesian((t * x(A1)) + ((1 - t) * x(A4)), (t * y(A1)) + ((1 - t) * y(A4)), t, 0, 1) → c4
  6. Textfield(F_1) → Fx
  7. Textfield(F_2) → Fy
  8. Sequence(Sequence[Vector[(j, k), (j + (scale * F_1(j, k)), k + (scale * F_2(j, k)))], j, xmin, xmax, xstep], k, ymin, ymax, ystep) → field, {{(NaN, NaN), (NaN, NaN), (NaN, NaN), (NaN, NaN), (NaN, NaN), (NaN, NaN), (NaN, NaN), (NaN, NaN), (NaN, NaN), (NaN, NaN)}, {(0, 0.5999692364897973), (0, 0.5999692364897973), (0, 0.5999692364897973), (0, 0.5999692364897973), (0, 0.5999692364897973), (0, 0.5999692364897973), (0, 0.5999692364897973), (0, 0.5999692364897973), (0, 0.5999692364897973), (0, 0.5999692364897973)}, {(0, 0.29998461824489864), (0, 0.29998461824489864), (0, 0.29998461824489864), (0, 0.29998461824489864), (0, 0.29998461824489864), (0, 0.29998461824489864), (0, 0.29998461824489864), (0, 0.29998461824489864), (0, 0.29998461824489864), (0, 0.29998461824489864)}, {(0, 0.1999897454965991), (0, 0.1999897454965991), (0, 0.1999897454965991), (0, 0.1999897454965991), (0, 0.1999897454965991), (0, 0.1999897454965991), (0, 0.1999897454965991), (0, 0.1999897454965991), (0, 0.1999897454965991), (0, 0.1999897454965991)}, {(0, 0.1499923091224491), (0, 0.1499923091224491), (0, 0.1499923091224491), (0, 0.1499923091224491), (0, 0.1499923091224491), (0, 0.1499923091224491), (0, 0.1499923091224491), (0, 0.1499923091224491), (0, 0.1499923091224491), (0, 0.1499923091224491)}, {(0, 0.11999384729795937), (0, 0.11999384729795937), (0, 0.11999384729795937), (0, 0.11999384729795937), (0, 0.11999384729795937), (0, 0.11999384729795937), (0, 0.11999384729795937), (0, 0.11999384729795937), (0, 0.11999384729795937), (0, 0.11999384729795937)}, {(0, 0.09999487274829955), (0, 0.09999487274829955), (0, 0.09999487274829955), (0, 0.09999487274829955), (0, 0.09999487274829955), (0, 0.09999487274829955), (0, 0.09999487274829955), (0, 0.09999487274829955), (0, 0.09999487274829955), (0, 0.09999487274829955)}, {(0, 0.0857098909271139), (0, 0.0857098909271139), (0, 0.0857098909271139), (0, 0.0857098909271139), (0, 0.0857098909271139), (0, 0.0857098909271139), (0, 0.0857098909271139), (0, 0.0857098909271139), (0, 0.0857098909271139), (0, 0.0857098909271139)}, {(0, 0.07499615456122477), (0, 0.07499615456122477), (0, 0.07499615456122477), (0, 0.07499615456122477), (0, 0.07499615456122477), (0, 0.07499615456122477), (0, 0.07499615456122477), (0, 0.07499615456122477), (0, 0.07499615456122477), (0, 0.07499615456122477)}, {(0, 0.06666324849886607), (0, 0.06666324849886607), (0, 0.06666324849886607), (0, 0.06666324849886607), (0, 0.06666324849886607), (0, 0.06666324849886607), (0, 0.06666324849886607), (0, 0.06666324849886607), (0, 0.06666324849886607), (0, 0.06666324849886607)}}
  9. Derivative(c1) → dc1
  10. Derivative(c2) → dc2
  11. Derivative(c3) → dc3
  12. Derivative(c4) → dc4
  13. Sum(Sequence[(((F_1(x(c1(i + dS / 2)), y(c1(i + dS / 2))), F_2(x(c1(i + dS / 2)), y(c1(i + dS / 2)))) * (y(dc1(i + dS / 2)), (-x(dc1(i + dS / 2))))) * dS), i, 0, s - dS, dS]) → Flux1
  14. Sum(Sequence[(((F_1(x(c2(i + dS / 2)), y(c2(i + dS / 2))), F_2(x(c2(i + dS / 2)), y(c2(i + dS / 2)))) * (y(dc2(i + dS / 2)), (-x(dc2(i + dS / 2))))) * dS), i, 0, s - dS, dS]) → Flux2
  15. Sum(Sequence[(((F_1(x(c3(i + dS / 2)), y(c3(i + dS / 2))), F_2(x(c3(i + dS / 2)), y(c3(i + dS / 2)))) * (y(dc3(i + dS / 2)), (-x(dc3(i + dS / 2))))) * dS), i, 0, s - dS, dS]) → Flux3
  16. Sum(Sequence[(((F_1(x(c4(i + dS / 2)), y(c4(i + dS / 2))), F_2(x(c4(i + dS / 2)), y(c4(i + dS / 2)))) * (y(dc4(i + dS / 2)), (-x(dc4(i + dS / 2))))) * dS), i, 0, s - dS, dS]) → Flux4
  17. Centroid(P1) → C1
  18. Derivative(F_1, x) → dxF_1
  19. Derivative(F_2, y) → dyF_2
  20. LaTeX(divVal, true, true) → text1
  21. Sequence(Vector[c1(s), c1(s) + ((scale * F_1(x(c1(s)), y(c1(s)))), (scale * F_2(x(c1(s)), y(c1(s)))))], s, 0.2, 0.8, 0.2) → vect1
  22. Sequence(Vector[c3(s), c3(s) + ((scale * F_1(x(c3(s)), y(c3(s)))), (scale * F_2(x(c3(s)), y(c3(s)))))], s, 0.2, 0.8, 0.2) → vect3
  23. Sequence(Vector[c4(s), c4(s) + ((scale * F_1(x(c4(s)), y(c4(s)))), (scale * F_2(x(c4(s)), y(c4(s)))))], s, 0.2, 0.8, 0.2) → vect4
  24. Sequence(Vector[c2(s), c2(s) + ((scale * F_1(x(c2(s)), y(c2(s)))), (scale * F_2(x(c2(s)), y(c2(s)))))], s, 0.2, 0.8, 0.2) → vect2

AI Drawing Prompt Reference

Draw a quadrilateral ABCD, connect its diagonals AC and BD. Take points E, F, G, H on AB, BC, CD, DA respectively, such that AE=EB, BF=FC, CG=GD, DH=HA. Draw the perpendicular bisectors of AB, BC, CD, DA, and mark the centroid of the quadrilateral. Calculate and display the area of the quadrilateral. Draw the gradient field of the quadrilateral.
The prompt above was compiled from the original drawing commands and is for reference only.