拉格朗日乘数法示例4

GeoGebra 命令及参数

1. Simplify(Derivative[f, y, 1]) → fy'
2. Simplify(Derivative[f, x, 1]) → fx'
3. LeftSide(Cu_g) → g
4. Simplify(Derivative[g, y, 1]) → gy'
5. Simplify(Derivative[g, x, 1]) → gx'
6. Point(Cu_g) → B
7. Vector(B, B + UnitVector[Vector[B, Dg]] / 3) → u_g
8. Vector(B, B + UnitVector[Vector[B, Df]] / 3) → u_f
9. Angle(u_g, u_f) → α
10. LaTeX(f, true) → text8a
11. LaTeX(Cu_g, true) → text8b
12. Textfield(f) → InputBox3
13. Textfield(Cu_g) → InputBox4
14. Zip((x(a), y(a), f(a)), a, Sequence[Point[Cu_g, t / n], t, 0, n]) → lg_1
15. Textfield(n) → InputBox5
16. CurveCartesian(sqrt(t), sqrt((1 - t^(3)) / 3), f(sqrt(t), sqrt((1 - t^(3)) / 3)), t, 0, 1) → q1
17. CurveCartesian((-sqrt(t)), sqrt((1 - t^(3)) / 3), f((-sqrt(t)), sqrt((1 - t^(3)) / 3)), t, 0, 1) → q2
18. Surface((1 - (3 * t^(2)))^(1 / 6), t, u, t, -1 / sqrt(3), 1 / sqrt(3), u, -1.2, 1.2) → g1
19. Surface((-(1 - (3 * t^(2)))^(1 / 6)), t, u, t, -1 / sqrt(3), 1 / sqrt(3), u, -1.2, 1.2) → g2
20. CurveCartesian((-sqrt(t)), (-sqrt((1 - t^(3)) / 3)), f((-sqrt(t)), (-sqrt((1 - t^(3)) / 3))), t, 0, 1) → q1a
21. CurveCartesian(sqrt(t), (-sqrt((1 - t^(3)) / 3)), f(sqrt(t), (-sqrt((1 - t^(3)) / 3))), t, 0, 1) → q2a
22. RotateText(text3, 90°) → text5
23. TableText(Append["N", 1…Length[l2]], Append["\fgcolor{red}{Cp}", l2], Append["\fgcolor{blue}{f}(\fgcolor{red}{C_p })", l2fa], Append["(\dot{f_x},\dot{f_y})", l2xy'_fa], Append["(\dot{g_x},\dot{g_y})", l2xy'_ga], Append["λ_x", lλ2ax], Append["λ_y", lλ2ay], Append["\widehat{\dot{g}\dot{f}} ", lα2], "c|_") → tTab2
24. Zip(Text["(" + (SurdText[x(a)]) + "," + (SurdText[y(a)]) + ")", (0, 0), true, true], a, l2) → l2surd
25. Zip(Text["(" + (SurdText[x(a), {sqrt(2), sqrt(3), sqrt(5), sqrt(10), cbrt(2), cbrt(3), cbrt(5)}]) + "," + (SurdText[y(a), {sqrt(2), sqrt(3), sqrt(5), sqrt(10), cbrt(2), cbrt(3), cbrt(5)}]) + ")", (0, 0), true, true], a, l1) → l1surd
26. TableText(Append["N", 1…Length[l1]], Append["\fgcolor{red}{Cp}", l1], Append["\fgcolor{blue}{f}(\fgcolor{red}{C_p })", l1fa], Append["(\dot{f_x},\dot{f_y})", l1xy'_fa], Append["(\dot{g_x},\dot{g_y})", l1xy'_ga], Append["λ_x", lλ1ax], Append["λ_y", lλ1ay], Append["\widehat{\dot{g}\dot{f}} ", lα1], "c|_") → tTab1
27. Segment(B, C) → f_1
28. Text("∇g", Point[u_g, 1]) → text25g
29. Text("∇f", Point[u_f, 1]) → text25f
30. Simplify(fx'(x, y) - (gx'(x, y) * fy'(x, y) / gy'(x, y))) → Cu_xf
31. Simplify(fy'(x, y) - (gy'(x, y) * fx'(x, y) / gx'(x, y))) → Cu_yf
32. RemoveUndefined(Zip[Vector[c, c + UnitVector[a] / 3], a, l1xy'_f, c, l1]) → lvec1_f
33. RemoveUndefined(Zip[Vector[c, c + UnitVector[a] / 3], a, l2xy'_f, c, l2]) → lvec2_f
34. RemoveUndefined(Zip[Vector[c, c + UnitVector[a] / 3], a, l1xy'_g, c, l1]) → lvec1_g
35. RemoveUndefined(Zip[Vector[c, c + UnitVector[a] / 3], a, l2xy'_g, c, l2]) → lvec2_g
36. Textfield(txtCu01_x) → InputBox1
37. Textfield(txtCu01_x) → InputBox2
38. Element(l1, Indexmax1) → Amax1_1
39. Element(l1, Indexmin1) → Amin1_1
40. Element(l2, Indexmin2) → Amin2_1
41. Zip(Segment[a, b], a, l1, b, l1f) → l1seg
42. Sequence(Text[i, l1(i) - (0.2, 0.1)], i, 1, lä1) → l1txt
43. Sequence(Text[i, l2(i) - (0.2, 0.1)], i, 1, lä2) → l2txt
44. Zip(Segment[a, b], a, l2, b, l2f) → l2seg
45. Element(l1f, Indexmax1) → Amax13d_1
46. Element(l2f, Indexmax2) → Amax23d_1
47. Element(l1f, Indexmin1) → Amin13d_1
48. Element(l2f, Indexmin2) → Amin23d_1
49. Element(l1f, 5) → Amin13d_2
50. Element(l1, 6) → Amax1_2
51. Element(l2, 6) → Amax2_2
52. Element(l2, Indexmax2) → Amax2_1
53. Element(l1f, 6) → Amax13d_2
54. Element(l2f, 6) → Amax23d_2
55. Element(l2f, 5) → Amin23d_2
56. Element(l1, 5) → Amin1_2
57. Element(l2, 5) → Amin2_2