In[16]:= f@x_, y_D = 6 - x^2 - y^2;

ParametricPlot3D@8r * Cos@tD, r * Sin@tD, 6 - r^2<, 8t, 0, 2 * Pi<, 8r, 0, 4<DContourPlot@f@x, yD, 8x, -4, 4<, 8y, -4, 4<Dgradf = 8D@f@x, yD, xD, D@f@x, yD, yD<;

8x0 = 2, y0 = 3<;

h = 0.01;

puntos = Table@8x1, y1< = 8x0, y0< + h * gradf �. 8x ® x0, y ® y0<;

8x0, y0< = 8x1, y1<, 8k, 1, 500<D

Out[17]=

-4

-2

0

2

4

-4

-2

0

2

4

-10

-5

0

5

Out[18]=

-4 -2 0 2 4

-4

-2

0

2

4

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80.259934, 0.389901<, 80.254736, 0.382103<, 80.249641, 0.374461<,

, , ,

2 Maximo_descenso_optimizacion.nb

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80.0111207, 0.016681<, 80.0108983, 0.0163474<, 80.0106803, 0.0160205<,

, , ,

Maximo_descenso_optimizacion.nb 3

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80.000475772, 0.000713659<, 80.000466257, 0.000699385<, 80.000456932, 0.000685398<,

, , ,

4 Maximo_descenso_optimizacion.nb

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80.000150413, 0.00022562<, 80.000147405, 0.000221107<, 80.000144457, 0.000216685<,

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80.000104557, 0.000156836<, 80.000102466, 0.000153699<, 80.000100417, 0.000150625<,

80.0000984086, 0.000147613<, 80.0000964405, 0.000144661<,

80.0000945116, 0.000141767<, 80.0000926214, 0.000138932<,

80.000090769, 0.000136153<, 80.0000889536, 0.00013343<,

80.0000871745, 0.000130762<, 80.000085431, 0.000128147<,

80.0000837224, 0.000125584<, 80.000082048, 0.000123072<<

In[13]:= c1 = ListPlot@puntos, Joined ® True, PlotStyle ® 8RGBColor@1, 0, 0D, Thickness@0.01D<Dc2 = ContourPlot@f@x, yD, 8x, -1, 1<,

8y, -1, 1<, ContourShading ® False, Contours ® 40DShow@c1, c2, AspectRatio ® AutomaticD

Out[13]=

0.2 0.4 0.6 0.8

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6 Maximo_descenso_optimizacion.nb