What is the extreme f(x,y)=5x^2+5y^2+5xy-10x-5y+18 ?

The extreme f(x,y)=5x^2+5y^2+5xy-10x-5y+18 is Minimum(1,0)

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extreme f(x,y)=5x^2+5y^2+5xy-10x-5y+18

extreme points

f (x, y) = 5 x^{2} + 5 y^{2} + 5 x y - 10 x - 5 y + 18

Minimum (1, 0)

Solution steps

Find the critical points:

(1, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 10

D (x, y) = 75

Check the sign of at each critical point

Check critical point

(1, 0) :

Minimum

Minimum (1, 0)

f (x, y) = x^{3} + 3 x y^{2} - 15 x^{2} - 15 y^{2} + 72 x

f (x, y) = 10 - 4 x - 5 y

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

f (x, y) = x^{2} - 3 x y + 6 y^{2} + 5 x - 2 y + 8

f (x) = x^{3} - 3 x^{2} + 4 x + 5

What is the extreme f(x,y)=5x^2+5y^2+5xy-10x-5y+18 ?
The extreme f(x,y)=5x^2+5y^2+5xy-10x-5y+18 is Minimum(1,0)