What is the extreme f(x,y)=3x^2-xy+y^2-11x ?

The extreme f(x,y)=3x^2-xy+y^2-11x is Minimum(2,1)

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extreme f(x,y)=3x^2-xy+y^2-11x

extreme points

f (x, y) = 3 x^{2} - x y + y^{2} - 11 x

Minimum (2, 1)

Solution steps

Find the critical points:

(2, 1)

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

D (x, y) = 11

Check the sign of at each critical point

Check critical point

(2, 1) :

Minimum

Minimum (2, 1)

f (x, y) = (x - 1)^{2} - (y - 1)^{2}

f (x, y) = x^{2} + y^{2} + 2 x - 18 y

f (x) = 161000 x - 100 x^{21}

f (x) = - 6 x^{2} e^{- x} - 4

f (x) = 2.2 + 2.6 x - 0.8 x^{2}

What is the extreme f(x,y)=3x^2-xy+y^2-11x ?
The extreme f(x,y)=3x^2-xy+y^2-11x is Minimum(2,1)