What is the extreme f(x,y)=2xy^2-2y^2-9x^2 ?

The extreme f(x,y)=2xy^2-2y^2-9x^2 is Maximum(0,0),Saddle(1,3),Saddle(1,-3)

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extreme f(x,y)=2xy^2-2y^2-9x^2

extreme points

f (x, y) = 2 x y^{2} - 2 y^{2} - 9 x^{2}

Maximum (0, 0), Saddle (1, 3), Saddle (1, - 3)

Solution steps

Find the critical points:

(0, 0), (1, 3), (1, - 3)

\frac{\partial ^{2} f}{\partial x ^{2}} = 4 x - 4

D (x, y) = - 18 (4 x - 4) - 16 y^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Check critical point

(1, 3) :

Saddle

Check critical point

(1, - 3) :

Saddle

Maximum (0, 0), Saddle (1, 3), Saddle (1, - 3)

f (x) = 3 x (x - 1)

f (x) = x - 2 x, (0, 9)

f (x) = 2 x^{3} + 6 x^{2} - 48 x + 6

- 80 e^{x} + 2 x e^{x} + 2 x^{2} e^{x} - 1

f (x) = x^{\frac{2}{3}} (\frac{5}{2} + x)

What is the extreme f(x,y)=2xy^2-2y^2-9x^2 ?
The extreme f(x,y)=2xy^2-2y^2-9x^2 is Maximum(0,0),Saddle(1,3),Saddle(1,-3)