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

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

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

extreme points

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

Maximum (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 y - 4) - 16 x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Check critical point

(1, 1) :

Saddle

Check critical point

(- 1, 1) :

Saddle

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

f (x) = 6 x^{2} + 7 y^{2}

f (x) = - 5 x^{2} + 10 x + 12

14400 + 700 x + x^{2}

f (x, y) = - 8 - 6 x + 3 x^{2} + 8 y + 5 y^{2}

f (x) = \frac{4 + x}{1 - x}, - 1 \leq x \leq 0

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