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

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

Popular >

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

extreme points

f (x, y) = x^{2} + x^{2} y + y^{2} + 1

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

Solution steps

Find the critical points:

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

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

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(2, - 1) :

Saddle

Check critical point

(- 2, - 1) :

Saddle

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

f (x) = 2 x + cos (x)

f (x) = (x^{2} + 1)^{3}

f (x) = x^{2} - 12 x

f (x, y) = \frac{1}{3} x^{3} + 2 y^{2} - 3 x^{2} + 5 x - 8 y + 4

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

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