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

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

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

extreme points

f (x, y) = 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) = - 1

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = 3 x^{2} - 5 x

f (x) = \frac{3}{7} (x^{2} - 1)^{\frac{2}{3}}

12 sin (3 x)

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

(x + 4)^{3} (3 x - 2)^{2}