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f(x,y,z) = -(x - 3 y)^2 - (2 x - z)^2 - (y - z)^2

f(x,y,z) = -x^2 + 6 x y - 9 y^2 - 4 x^2 + 4 x z - z^2 - y^2 + 2 y z - z^2

f(x,y,z) = -5 x^2 - 10 y^2 - 2 z^2 + 6 x y + 4 x z + 2 y z

Derivadas primeras

∂f/∂x = -2(x - 3y) - 2(2)(2x - z) = -10 x + 6 y + 4 z

∂f/∂y = -2(-3)(x - 3y) - 2(y - z) = 6 x - 20 y + 2 z

∂f/∂z = -2(-1)(2x - z) - 2(-1)(y - z) = 4 x + 2 y - 4 z

Derivadas segundas

∂^2f/∂x^2 = -10

∂^2f/∂x∂y = 6

∂^2f/∂x∂z = 4

∂^2f/∂y∂x = 6

∂^2f/∂y^2 = -20

∂^2f/∂y∂z = 2

∂^2f/∂z∂x = 4

∂^2f/∂z∂y = 2

∂^2f/∂z^2 = -4

La matriz hessiana

A =

...-10....6.......4

....6.....-20....2

...4......2......-4

D11 = -10

D22 =

...-10....6

....6....-20

D22 = 164

D33 =

...-10....6.......4

....6.....-20....2

...4......2......-4

= -200

La forma es definida NEGATIVA

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