使用Hessian矩阵寻找并判断临界点 by Roman Chijner

GeoGebra 命令及参数

1. Simplify(Derivative[f, y, 1]) → fy
2. Simplify(Derivative[fy, x, 1]) → fyx
3. Simplify(Derivative[fy, y, 1]) → fyy
4. Simplify(Derivative[f, x, 1]) → fx
5. Simplify(Derivative[fx, y, 1]) → fxy
6. Simplify(Derivative[fx, x, 1]) → fxx
7. ImplicitCurve(fx(x, y)) → ax
8. ImplicitCurve(fy(x, y)) → ay
9. Zip({{fxx(a), fxy(a)}, {fyx(a), fyy(a)}}, a, l1a) → M
10. Zip(Determinant[a], a, M) → D
11. Zip(fxx(a), a, l1a) → f_{xx}
12. Sequence(If[D(i) > 0, If[f_{xx}(i) > 0, "local minimum", "local maximum"], "saddle point"], i, 1, Length[l1a]) → l4
13. Zip((x(a), y(a), f(a)), a, l1a) → l5
14. Zip(fx(a), a, l1a) → lfx
15. Zip(fy(a), a, l1a) → lfy
16. LaTeX(f, true) → text2
17. RotateText(txt1, 90°) → txt2
18. TableText(Append["i", 1…Length[l5]], Append["critical points", l5], Append["f_{x}", lfx], Append["f_{y}", lfy], Append["f_{xx}", f_{xx}], Append["Det", D], Append["", l4], "v") → text1