What is the extreme 2x^2-2x^2y+y^2 ?

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

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extreme 2x^2-2x^2y+y^2

extreme points

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

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

Solution steps

Find the critical points:

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

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

D (x, y) = 2 (4 - 4 y) - 16 x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(1, 1) :

Saddle

Check critical point

(- 1, 1) :

Saddle

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

x^{2} + x + 2

\frac{x - 5}{x ^{2} - 18 x + 81}

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

x^{6} - \frac{6}{5} x^{5}

P (x, y) = 0.3 + x^{2} + 0.2 y^{2} + 0.1 x y - 14 x - 10 y + 2000

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