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

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

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

extreme points

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

Minimum (3, 1)

Solution steps

Find the critical points:

(3, 1)

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

D (x, y) = 28

Check the sign of at each critical point

Check critical point

(3, 1) :

Minimum

Minimum (3, 1)

f (x) = \frac{7 x}{x ^{2} + 9}, 0 \leq x \leq 9

2 x^{3} + 4 x^{2} - 1

f (x) = x \cdot (ln (x))^{5}

f (x, y) = 40000 x + 30000 y - 8 x^{2} - 15 y^{2} - 10 x y

f (x) = e^{x^{3} - 3 x}

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