What is the extreme 4xy+x^4+y^4 ?

The extreme 4xy+x^4+y^4 is Saddle(0,0)

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extreme 4xy+x^4+y^4

extreme points

4 x y + x^{4} + y^{4}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 12 y^{2}

D (x, y) = 144 x^{2} y^{2} - 16

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

y = x^{3} - 3 x^{2} - 9 x + 1

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

y = \frac{9 x}{x ^{2} + 1}

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

f (x) = \frac{ln ∣ x ∣}{x}, (- 3, 0)