What is the extreme f(x,y)=x^2+xy+y^2-12x-24y-241 ?

The extreme f(x,y)=x^2+xy+y^2-12x-24y-241 is Minimum(0,12)

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extreme f(x,y)=x^2+xy+y^2-12x-24y-241

extreme points

f (x, y) = x^{2} + x y + y^{2} - 12 x - 24 y - 241

Minimum (0, 12)

Solution steps

Find the critical points:

(0, 12)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(0, 12) :

Minimum

Minimum (0, 12)

y (x, t) = x (t - \frac{1}{4})

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

f (x) = x^{3} + 9 x^{2} + 27 x + 3

f (x, y) = x^{2} - 12 x y + 2 y^{4}

f (x, y) = - x^{3} + y^{2} + 3 x - 4 y - 1

What is the extreme f(x,y)=x^2+xy+y^2-12x-24y-241 ?
The extreme f(x,y)=x^2+xy+y^2-12x-24y-241 is Minimum(0,12)