What is the extreme f(x,y)=x^2+xy-10x+y^2-11y+37 ?

The extreme f(x,y)=x^2+xy-10x+y^2-11y+37 is Minimum(3,4)

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extreme f(x,y)=x^2+xy-10x+y^2-11y+37

extreme points

f (x, y) = x^{2} + x y - 10 x + y^{2} - 11 y + 37

Minimum (3, 4)

Solution steps

Find the critical points:

(3, 4)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(3, 4) :

Minimum

Minimum (3, 4)

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

f (x) = (x - 4) (x + 1) (x + 5)

f (x) = \frac{t}{t - 2}

f (x) = \frac{x ^{2} - 4}{x ^{2} + 1}

f (x) = x^{3} - 6 x^{2} + 8, - 4 \leq x \leq 1

What is the extreme f(x,y)=x^2+xy-10x+y^2-11y+37 ?
The extreme f(x,y)=x^2+xy-10x+y^2-11y+37 is Minimum(3,4)