What is the extreme f(x,y)=x^2-xy+y^2-9x+6y+8 ?

The extreme f(x,y)=x^2-xy+y^2-9x+6y+8 is Minimum(4,-1)

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extreme f(x,y)=x^2-xy+y^2-9x+6y+8

extreme points

f (x, y) = x^{2} - x y + y^{2} - 9 x + 6 y + 8

Minimum (4, - 1)

Solution steps

Find the critical points:

(4, - 1)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(4, - 1) :

Minimum

Minimum (4, - 1)

- x^{2} ln (x)

f (x) = \frac{3}{4 x ^{4} - 8 x ^{2}}

f (x) = x^{3} - 45 x^{2} + 243 x + 30000

f (x) = x^{3} - 27 x, - 2 \leq x \leq 4

- 7 x + 2

What is the extreme f(x,y)=x^2-xy+y^2-9x+6y+8 ?
The extreme f(x,y)=x^2-xy+y^2-9x+6y+8 is Minimum(4,-1)