What is the extreme f(x,y)=2x^2+3xy+y^2+ax+5 ?

The extreme f(x,y)=2x^2+3xy+y^2+ax+5 is Saddle(2a,-3a)

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extreme f(x,y)=2x^2+3xy+y^2+ax+5

extreme points

f (x, y) = 2 x^{2} + 3 x y + y^{2} + a x + 5

Saddle (2 a, - 3 a)

Solution steps

Find the critical points:

(2 a, - 3 a)

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

D (x, y) = - 1

Check the sign of at each critical point

Check critical point

(2 a, - 3 a) :

Saddle

Saddle (2 a, - 3 a)

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

f (x) = 2 x^{2} - 4 x - 1

f (x) = 3 x^{4} + 16 x^{3} + 24 x^{2} + 32

\frac{x ^{2}}{x ^{2} + 3}

f (x) = 88 - \frac{1}{2} x - \frac{3200}{x}

What is the extreme f(x,y)=2x^2+3xy+y^2+ax+5 ?
The extreme f(x,y)=2x^2+3xy+y^2+ax+5 is Saddle(2a,-3a)