What is the extreme f(x,y)=x^2y+y^2+8x ?

The extreme f(x,y)=x^2y+y^2+8x is Saddle(2,-2)

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extreme f(x,y)=x^2y+y^2+8x

extreme

Saddle (2, - 2)

Solution steps

Find the critical points:

(2, - 2)

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

D (x, y) = 4 y - 4 x^{2}

Check the sign of at each critical point

Check critical point

(2, - 2) :

Saddle

Saddle (2, - 2)

What is the extreme f(x,y)=x^2y+y^2+8x ?
The extreme f(x,y)=x^2y+y^2+8x is Saddle(2,-2)