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(5/3 , 4/3)

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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 (\frac{5}{3}, \frac{4}{3})

Solution steps

Find the critical points:

(\frac{5}{3}, \frac{4}{3})

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

D (x, y) = 75

Check the sign of at each critical point

Check critical point

(\frac{5}{3}, \frac{4}{3}) :

Minimum

Minimum (\frac{5}{3}, \frac{4}{3})

f (x) = 355 x^{2} - 1420 x^{3}

6 + 9 x^{2} - 6 x^{3}

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

f (x) = 2 x + 4 sin (x)

f (x) = x^{2} - 6 x - 8

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(5/3 , 4/3)