What is the extreme f(x,y)=2x^2+2xy+3y^2-16x-18y+54 ?

The extreme f(x,y)=2x^2+2xy+3y^2-16x-18y+54 is Minimum(3,2)

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extreme f(x,y)=2x^2+2xy+3y^2-16x-18y+54

extreme points

f (x, y) = 2 x^{2} + 2 x y + 3 y^{2} - 16 x - 18 y + 54

Minimum (3, 2)

Solution steps

Find the critical points:

(3, 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = 6

D (x, y) = 20

Check the sign of at each critical point

Check critical point

(3, 2) :

Minimum

Minimum (3, 2)

+ x^{3} + 4

y = \frac{32 x}{x ^{2} + 16}

y = 2 x - 7 ln (x)

f (x) = (x + 2) (x + 7)

f (x) = - 2.3

What is the extreme f(x,y)=2x^2+2xy+3y^2-16x-18y+54 ?
The extreme f(x,y)=2x^2+2xy+3y^2-16x-18y+54 is Minimum(3,2)