几何中值与海森矩阵下的临界点

GeoGebra 命令及参数

1. Polygon({((-π), ((-π)) / 2), ((-π), π / 2), (π, π / 2), (π, ((-π)) / 2)}) → q
2. PointIn(q) → P9
3. PointIn(q) → A_2
4. Sequence(If[D(i) > 0, If[f_{xx}(i) > 0, "local minimum", "local maximum"], If[(D(i) * f_{xx}(i)) ≟ 0, "?", "saddle point"]], i, 1, Length[l1]) → l4
5. Zip((x(a), y(a)), a, l1) → l5
6. TableText(Append["i", 1…Length[l1]], Append["critical points", l5], Append["f_{x}", lfx], Append["f_{y}", lfy], Append["f_{xx}", f_{xx}], Append["Det", D], Append["", l4], "v") → text1
7. Function((q_f * f(u, v)) + b_0, u, (-π), π, v, ((-π)) / 2, π / 2) → f0
8. Length(lsad) → läsad
9. Length(lmax) → lämax
10. Length(lmin) → lämin
11. Zip(Segment[A, p], p, lP) → seg
12. Sum(seg) → sum_seg
13. Flatten(Sequence[Sequence[((-π) + ((2 * π / na) * i), ((-π)) / 2 + (π / na * j)), j, 1, na - 1], i, 1, na - 1]) → ltest_2
14. Zip((R; x(a); y(a)), a, ltest_2) → ltest_3
15. TableText(Append["i", Sequence[Length[lmax]]], Append["P_{Max }\;(φ,θ)", lmax], Append["(f'x,f'y)", lZf'xymax], "v") → textmax
16. TableText(Append["i", Sequence[Length[(lmin * x)]]], Append["P_{Max }\;(φ,θ)", lmin], Append["(f'x,f'y)", lZf'xymin], "v") → textmin
17. TableText(Append["i", Sequence[Length[(lsad * x)]]], Append["P_{Max }\;(φ,θ)", lsad], Append["(f'x,f'y)", lZf'xysad], "v") → textsad
18. Textfield(R) → InputBox1
19. Textfield(n) → InputBox2
20. Textfield(lP) → InputBox3