What is the extreme f(x,y)=2x^2+3xy+4y^2+6x-7y ?

The extreme f(x,y)=2x^2+3xy+4y^2+6x-7y is Minimum(-3,2)

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extreme f(x,y)=2x^2+3xy+4y^2+6x-7y

extreme points

f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} + 6 x - 7 y

Minimum (- 3, 2)

Solution steps

Find the critical points:

(- 3, 2)

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

D (x, y) = 23

Check the sign of at each critical point

Check critical point

(- 3, 2) :

Minimum

Minimum (- 3, 2)

y = x e^{\frac{x}{2}}

f (x) = x^{4} - 62 x^{2} + 120 x + 9

f (x) = 9 x^{2} - 36 x + 27

4 x^{2}

f (x, y) = - 5 y^{2} - 6 x^{3} + 12 x^{2}

What is the extreme f(x,y)=2x^2+3xy+4y^2+6x-7y ?
The extreme f(x,y)=2x^2+3xy+4y^2+6x-7y is Minimum(-3,2)