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

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

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

extreme points

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

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

Solution steps

Find the critical points:

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

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

D (x, y) = - 8 y - 16 x^{2}

Check the sign of at each critical point

Check critical point

(0, - 1) :

Minimum

Check critical point

(1, 0) :

Saddle

Check critical point

(- 1, 0) :

Saddle

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

P (a, b) = a^{2} - 6 a + 9 - b^{2}

f (x, y) = x^{3} + y^{3} + 15 x y

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

f (x) = x ln (\frac{x}{3}), 0.1 \leq x \leq 3

f (x) = 2 x^{3} - 6 x^{2} + 6 x - 8

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