What is the extreme f(x,y)=2x^3+y^3+3x^2-3y^2-16 ?

The extreme f(x,y)=2x^3+y^3+3x^2-3y^2-16 is Minimum(0,2),Saddle(0,0),Saddle(-1,2),Maximum(-1,0)

Popular >

extreme f(x,y)=2x^3+y^3+3x^2-3y^2-16

extreme points

f (x, y) = 2 x^{3} + y^{3} + 3 x^{2} - 3 y^{2} - 16

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

Solution steps

Find the critical points:

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

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

D (x, y) = (6 y - 6) (12 x + 6)

Check the sign of at each critical point

Check critical point

(0, 2) :

Minimum

Check critical point

(0, 0) :

Saddle

Check critical point

(- 1, 2) :

Saddle

Check critical point

(- 1, 0) :

Maximum

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

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

f (x) = - x^{2} - x + 1

f (x, y) = 5 x^{2} + 3 x y + 10 y^{2} + 4 x y^{2} + 6 x^{2} y

f (x) = 8 (x y) - 2 x^{4} - 2 y^{4}

f (x) = 3 x^{3} + 3 x^{2} - 10 x - 2

What is the extreme f(x,y)=2x^3+y^3+3x^2-3y^2-16 ?
The extreme f(x,y)=2x^3+y^3+3x^2-3y^2-16 is Minimum(0,2),Saddle(0,0),Saddle(-1,2),Maximum(-1,0)