What is the extreme x^2+6xy+2y^2 ?

The extreme x^2+6xy+2y^2 is Saddle(0,0)

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extreme x^2+6xy+2y^2

extreme points

x^{2} + 6 x y + 2 y^{2}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 4

D (x, y) = - 28

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

+ \frac{x + \frac{1}{x} + 8}{x + \frac{1}{x} + 2}

f (x, y) = 6 (1 - x^{(2)}) \cdot (1 - y^{(2)})

f (x) = - 2 x^{2} ln (x) + 17 x^{2}

∣ x + 4 ∣

f (x) = \frac{2 x ^{2} + 3}{x ^{2} - 1}