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

The extreme f(x,y)=(x^2-y^2)e-(x^2+y^2) is Saddle(0,0)

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extreme f(x,y)=(x^2-y^2)e-(x^2+y^2)

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = (2 e - 2) (- 2 e - 2)

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

y = \frac{x \cdot ( 1 + x ) \cdot ( 1 - x )}{1 + 2 x}

f (x) = \frac{( x ^{2} )}{x ^{2} - 81}

f (x) = 3 x^{3} - 12 x^{2} + 12 x - 6, 0 \leq x \leq 4

y = 3 x^{3} (x - 5)^{2}

y = \frac{1}{x - 8} - 9

What is the extreme f(x,y)=(x^2-y^2)e-(x^2+y^2) ?
The extreme f(x,y)=(x^2-y^2)e-(x^2+y^2) is Saddle(0,0)