What is the extreme f(x,y)=3xy-x^2y-xy^2 ?

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

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extreme f(x,y)=3xy-x^2y-xy^2

extreme points

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

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

Solution steps

Find the critical points:

(0, 3), (1, 1)

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

D (x, y) = - 4 x y + 12 x - 4 x^{2} + 12 y - 4 y^{2} - 9

Check the sign of at each critical point

Check critical point

(0, 3) :

Saddle

Check critical point

(1, 1) :

Maximum

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

y = x^{3} - 3 x^{2} + 3

f (x, y) = 48 - 3 x^{2} - 3 y^{2}

f (x) = \frac{x}{x ^{2} + 16}

f (x) = x e^{6 x^{2}}

f (x) = 2 x^{3} - 6 x + 4

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