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

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

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

extreme points

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

Saddle (0, 1), Maximum (- \frac{1}{3}, \frac{1}{3})

Solution steps

Find the critical points:

(0, 1), (- \frac{1}{3}, \frac{1}{3})

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

D (x, y) = 4 x y - 4 x - 4 x^{2} - 4 y^{2} + 4 y - 1

Check the sign of at each critical point

Check critical point

(0, 1) :

Saddle

Check critical point

(- \frac{1}{3}, \frac{1}{3}) :

Maximum

Saddle (0, 1), Maximum (- \frac{1}{3}, \frac{1}{3})

- 7 x^{2} + 126 x - 560

20 - 0.06 x + 0.0002 x^{2}

f (x) = 2 x - 5 x^{2}

2 x^{2} - 4 x + 1

f (x) = y^{2} + y^{2} \cdot x + 3 x - 8

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