What is the extreme 2y^3+6yx^2-3x^3-150y ?

The extreme 2y^3+6yx^2-3x^3-150y is Saddle(3,4),Saddle(-3,-4)

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extreme 2y^3+6yx^2-3x^3-150y

extreme points

2 y^{3} + 6 y x^{2} - 3 x^{3} - 150 y

Saddle (3, 4), Saddle (- 3, - 4)

Solution steps

Find the critical points:

(3, 4), (- 3, - 4)

\frac{\partial ^{2} f}{\partial y ^{2}} = - 18 x + 12 y

D (y, x) = 12 y (- 18 x + 12 y) - 144 x^{2}

Check the sign of at each critical point

Check critical point

(3, 4) :

Saddle

Check critical point

(- 3, - 4) :

Saddle

Saddle (3, 4), Saddle (- 3, - 4)

What is the extreme 2y^3+6yx^2-3x^3-150y ?
The extreme 2y^3+6yx^2-3x^3-150y is Saddle(3,4),Saddle(-3,-4)