What is the extreme f(x,y)= 1/4 x^4-1/2 x^2+y^2 ?

The extreme f(x,y)= 1/4 x^4-1/2 x^2+y^2 is Saddle(0,0),Minimum(-1,0),Minimum(1,0)

Popular >

extreme f(x,y)= 1/4 x^4-1/2 x^2+y^2

extreme points

f (x, y) = \frac{1}{4} x^{4} - \frac{1}{2} x^{2} + y^{2}

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

Solution steps

Find the critical points:

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

\frac{\partial ^{2} f}{\partial x ^{2}} = 2

D (x, y) = 2 (3 x^{2} - 1)

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(- 1, 0) :

Minimum

Check critical point

(1, 0) :

Minimum

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

f (x) = x + \frac{4}{x ^{2}}

f (x) = (x - 2) (x + 1) (x + 4)

f (x) = x^{3} - 3 x - 3

x^{2} + y^{2} - x y

f (x) = 14 x^{2} - 2 x^{3} + 4 x y

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