What is the extreme f(x,y)=45x+15y^2-15x^2-5y^3-5x^3 ?

The extreme f(x,y)=45x+15y^2-15x^2-5y^3-5x^3 is Saddle(1,0),Maximum(1,2),Minimum(-3,0),Saddle(-3,2)

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extreme f(x,y)=45x+15y^2-15x^2-5y^3-5x^3

extreme points

f (x, y) = 45 x + 15 y^{2} - 15 x^{2} - 5 y^{3} - 5 x^{3}

Saddle (1, 0), Maximum (1, 2), Minimum (- 3, 0), Saddle (- 3, 2)

Solution steps

Find the critical points:

(1, 0), (1, 2), (- 3, 0), (- 3, 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 30 y + 30

D (x, y) = (- 30 x - 30) (- 30 y + 30)

Check the sign of at each critical point

Check critical point

(1, 0) :

Saddle

Check critical point

(1, 2) :

Maximum

Check critical point

(- 3, 0) :

Minimum

Check critical point

(- 3, 2) :

Saddle

Saddle (1, 0), Maximum (1, 2), Minimum (- 3, 0), Saddle (- 3, 2)

What is the extreme f(x,y)=45x+15y^2-15x^2-5y^3-5x^3 ?
The extreme f(x,y)=45x+15y^2-15x^2-5y^3-5x^3 is Saddle(1,0),Maximum(1,2),Minimum(-3,0),Saddle(-3,2)