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

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

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

extreme points

f (x, y) = x + y + x 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) = 1 + \frac{5}{x} - \frac{8}{x ^{2}}

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

y = 3 x - x^{3}

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

f (x) = \frac{x ^{2} - 4}{x ^{2} + 4}, - 4 \leq x \leq 4