What is the extreme f(x,y)=2x^2-xy+y^2-6x-9y+7 ?

The extreme f(x,y)=2x^2-xy+y^2-6x-9y+7 is Minimum(3,6)

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extreme f(x,y)=2x^2-xy+y^2-6x-9y+7

extreme points

f (x, y) = 2 x^{2} - x y + y^{2} - 6 x - 9 y + 7

Minimum (3, 6)

Solution steps

Find the critical points:

(3, 6)

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

D (x, y) = 7

Check the sign of at each critical point

Check critical point

(3, 6) :

Minimum

Minimum (3, 6)

12 x^{\frac{2}{3}} - 8 x

f (x) = 9 - x^{2}, - 3 \leq x \leq 2

f (x) = \frac{1}{x} - \frac{64}{y} + x y

f (x) = x^{2} + 8 x + 13

f (x) = 15 x^{4} - 4 x^{3}

What is the extreme f(x,y)=2x^2-xy+y^2-6x-9y+7 ?
The extreme f(x,y)=2x^2-xy+y^2-6x-9y+7 is Minimum(3,6)