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

The extreme f(x,y)=xy+1x+1y is Saddle(-1,-1)

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

extreme points

f (x, y) = x y + 1 x + 1 y

Saddle (- 1, - 1)

Solution steps

Find the critical points:

(- 1, - 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, y) = - 1

Check the sign of at each critical point

Check critical point

(- 1, - 1) :

Saddle

Saddle (- 1, - 1)

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

P (x, y) = 30 x^{2} + 2 x y - 4 y^{2} + 47 x - 12 y + 7

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

f (x) = 2 x^{2} + 8 x

f (x) = x^{\frac{3}{5}} (4 - x)

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