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

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

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

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = - 96

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = 14 + 4 x - x^{2}

f (x, y) = x^{3} + x y^{2} + y^{2} - 4 y + 11

8 + 2 x - 2 x^{2}

f (x, y) = 10 x^{2} + 7 x y + 8 y^{2} + 8 x y^{2} + 9 x^{2} y

f (x) = 9 - x, - 1 \leq x \leq 3

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