What is the extreme f(x,y)=2x^3+3x^3y^2-4x^2y^2-2y ?

The extreme f(x,y)=2x^3+3x^3y^2-4x^2y^2-2y is Saddle(0.61561…,-1.22548…)

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extreme f(x,y)=2x^3+3x^3y^2-4x^2y^2-2y

extreme points

f (x, y) = 2 x^{3} + 3 x^{3} y^{2} - 4 x^{2} y^{2} - 2 y

Saddle (0.61561 \dots, - 1.22548 \dots)

Solution steps

Find the critical points:

(0.61561 \dots, - 1.22548 \dots)

\frac{\partial ^{2} f}{\partial x ^{2}} = 6 x^{3} - 8 x^{2}

D (x, y) = - 216 x^{4} y^{2} + 72 x^{4} + 384 x^{3} y^{2} - 96 x^{3} - 192 x^{2} y^{2}

Check the sign of at each critical point

Check critical point

(0.61561 \dots, - 1.22548 \dots) :

Saddle

Saddle (0.61561 \dots, - 1.22548 \dots)

f (x) = e^{x} - 7 e^{- x} - 8 x

e^{- x^{2}} - 2 e^{- x^{2}} x^{2}

f (x) = x^{11} - 3 x^{9} + 2

f (x, y) = - 2.8 + x^{2} - 6.4 x y + 1.4 y^{2}

f (x, y) = 4 x y + x^{4} + y^{4}

What is the extreme f(x,y)=2x^3+3x^3y^2-4x^2y^2-2y ?
The extreme f(x,y)=2x^3+3x^3y^2-4x^2y^2-2y is Saddle(0.61561…,-1.22548…)