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

The extreme f(x,y)=2x^2+xy+y^2-x-3y is Minimum(-1/7 , 11/7)

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

extreme points

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

Minimum (- \frac{1}{7}, \frac{11}{7})

Solution steps

Find the critical points:

(- \frac{1}{7}, \frac{11}{7})

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

D (x, y) = 7

Check the sign of at each critical point

Check critical point

(- \frac{1}{7}, \frac{11}{7}) :

Minimum

Minimum (- \frac{1}{7}, \frac{11}{7})

f (t) = (4 - t) 4^{t}

f (x) = 2 x^{3} - 15 x^{2} - 30

f (x) = 15 x^{2} - 15 x^{4}

6 x^{3} - 9 x^{2} - 216 x + 9

f (x) = \frac{x ^{4}}{4} + \frac{5}{3} x^{3} - 5 x^{2} - 50 x + 1

What is the extreme f(x,y)=2x^2+xy+y^2-x-3y ?
The extreme f(x,y)=2x^2+xy+y^2-x-3y is Minimum(-1/7 , 11/7)