What is the extreme f(x,y)=-150x+2x^3+6xy^2-3y^3 ?

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

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extreme f(x,y)=-150x+2x^3+6xy^2-3y^3

extreme points

f (x, y) = - 150 x + 2 x^{3} + 6 x y^{2} - 3 y^{3}

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

Solution steps

Find the critical points:

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

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

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

f (x) = x^{1} - (4 cos (x))

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

f (x) = 5 x ln (x)

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

f (x, y) = 9 e^{4 y - x^{2} - y^{2}}

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