What is the extreme f(x,y)=(x+y-1)*xy ?

The extreme f(x,y)=(x+y-1)*xy is Saddle(0,1),Minimum(1/3 , 1/3)

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extreme f(x,y)=(x+y-1)*xy

extreme points

f (x, y) = (x + y - 1) \cdot x y

Saddle (0, 1), Minimum (\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^{2} + 4 x - 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}) :

Minimum

Saddle (0, 1), Minimum (\frac{1}{3}, \frac{1}{3})

f (x) = x^{3} + x^{2} - 5 x - 4

f (x) = x 36 - x^{2}, - 6 \leq x \leq 6

f (x) = 5 x y

f (x, y) = x^{3} + y^{3} - 192 x - 300 y + 2

f (x) = \frac{4 x ^{2}}{x ^{2} + 3}

What is the extreme f(x,y)=(x+y-1)*xy ?
The extreme f(x,y)=(x+y-1)*xy is Saddle(0,1),Minimum(1/3 , 1/3)