What is the extreme f(x,y)=9x^2+xy+10y^2 ?

The extreme f(x,y)=9x^2+xy+10y^2 is Minimum(0,0)

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extreme f(x,y)=9x^2+xy+10y^2

extreme points

f (x, y) = 9 x^{2} + x y + 10 y^{2}

Minimum (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 20

D (x, y) = 359

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Minimum (0, 0)

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

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

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

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

f (x) = 6 x^{5} - 2 x^{4}

What is the extreme f(x,y)=9x^2+xy+10y^2 ?
The extreme f(x,y)=9x^2+xy+10y^2 is Minimum(0,0)