What is the extreme f(x,y)=-14+5*x^2+x*y+y^2 ?

The extreme f(x,y)=-14+5*x^2+x*y+y^2 is Minimum(0,0)

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extreme f(x,y)=-14+5x^2+xy+y^2

extreme points

f (x, y) = - 14 + 5 \cdot x^{2} + x \cdot y + y^{2}

Minimum (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = 19

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Minimum (0, 0)

f (x) = 5 x + \frac{3}{x}

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

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

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

2 x^{2} + 4 x + 1

What is the extreme f(x,y)=-14+5*x^2+x*y+y^2 ?
The extreme f(x,y)=-14+5*x^2+x*y+y^2 is Minimum(0,0)