What is the extreme f(x,y)=2x^2+3xy+4y^2+5x-2y ?

The extreme f(x,y)=2x^2+3xy+4y^2+5x-2y is Minimum(-2,1)

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extreme f(x,y)=2x^2+3xy+4y^2+5x-2y

extreme points

f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} + 5 x - 2 y

Minimum (- 2, 1)

Solution steps

Find the critical points:

(- 2, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 8

D (x, y) = 23

Check the sign of at each critical point

Check critical point

(- 2, 1) :

Minimum

Minimum (- 2, 1)

What is the extreme f(x,y)=2x^2+3xy+4y^2+5x-2y ?
The extreme f(x,y)=2x^2+3xy+4y^2+5x-2y is Minimum(-2,1)