利用海森矩阵找极值点及其性质

GeoGebra 命令及参数

1. Simplify(Derivative[f, x, 1]) → fx
2. Simplify(Derivative[fx, x, 1]) → fxx
3. Simplify(Derivative[fx, y, 1]) → fxy
4. Simplify(Derivative[f, y, 1]) → fy
5. Simplify(Derivative[fy, y, 1]) → fyy
6. Simplify(Derivative[fy, x, 1]) → fyx
7. Zip({{fxx(a), fxy(a)}, {fyx(a), fyy(a)}}, a, l1) → M
8. Zip(Determinant[a], a, M) → D
9. Zip(fxx(a), a, l1) → f_{xx}
10. Sequence(If[D(i) > 0, If[f_{xx}(i) > 0, "local minimum", "local maximum"], "saddle point"], i, 1, Length[l1]) → l4
11. Zip((x(a), y(a), f(a)), a, l1) → l5
12. Zip(fx(a), a, l1) → lfx
13. Zip(fy(a), a, l1) → lfy
14. 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
15. LaTeX(f, true) → text3
16. RotateText(txt1, 90°) → txt2