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

The extreme f(x,y)=x(y+1)+(x+y+1) is Saddle(-1,-2)

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

extreme points

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

Saddle (- 1, - 2)

Solution steps

Find the critical points:

(- 1, - 2)

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

D (x, y) = - 1

Check the sign of at each critical point

Check critical point

(- 1, - 2) :

Saddle

Saddle (- 1, - 2)

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

f (x) = \frac{25}{2} x^{2} - ln (x)

f (x) = - 2 x^{3} + 33 x^{2} - 144 x + 1

y = - 2 x^{2} - 3 x + 1

f (x) = 4 x^{3} ln (4 x)

What is the extreme f(x,y)=x(y+1)+(x+y+1) ?
The extreme f(x,y)=x(y+1)+(x+y+1) is Saddle(-1,-2)