What is the extreme f(x,y)=4x^2+2y^2-2xy-10y-2x ?

The extreme f(x,y)=4x^2+2y^2-2xy-10y-2x is Minimum(1,3)

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extreme f(x,y)=4x^2+2y^2-2xy-10y-2x

extreme points

f (x, y) = 4 x^{2} + 2 y^{2} - 2 x y - 10 y - 2 x

Minimum (1, 3)

Solution steps

Find the critical points:

(1, 3)

\frac{\partial ^{2} f}{\partial x ^{2}} = 4

D (x, y) = 28

Check the sign of at each critical point

Check critical point

(1, 3) :

Minimum

Minimum (1, 3)

(x - y) (9 - x y)

f (x) = 15 x^{4} + 8 x^{3} - 18 x^{2} + 1

f (x) = e^{x y}

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

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

What is the extreme f(x,y)=4x^2+2y^2-2xy-10y-2x ?
The extreme f(x,y)=4x^2+2y^2-2xy-10y-2x is Minimum(1,3)