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

The extreme f(x,y)=4xy-y^4-2x^2 is Saddle(0,0),Maximum(-1,-1),Maximum(1,1)

Popular >

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

extreme points

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

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

Solution steps

Find the critical points:

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

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

D (x, y) = 48 y^{2} - 16

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(- 1, - 1) :

Maximum

Check critical point

(1, 1) :

Maximum

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

f (x, y) = 2 x^{3} - 6 x^{2} + y^{3} + 21 y^{2}

x^{2} - 4 x + 3

f (x) = x^{3} + x^{2} - 5

f (x, y) = 25 - x^{2} - y^{2}

- 7 (x + 3)^{2} (x - 1) (x - 5)

What is the extreme f(x,y)=4xy-y^4-2x^2 ?
The extreme f(x,y)=4xy-y^4-2x^2 is Saddle(0,0),Maximum(-1,-1),Maximum(1,1)