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

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

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

extreme points

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

Minimum (2, 3)

Solution steps

Find the critical points:

(2, 3)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(2, 3) :

Minimum

Minimum (2, 3)

f (x) = 4 x^{3} - x^{2} + 9

x^{2} - 6 x + 12

f (x) = \cdot f (y) - f (x, y) (x y) = 3 x + 3 y + 6

f (x) = 3 - sin (3 x)

f (x) = x^{2} - 7 x + 10

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