What is the extreme f(x,y)=x^2y-15xy^2+12y ?

The extreme f(x,y)=x^2y-15xy^2+12y is Saddle(-2,-4/15),Saddle(2, 4/15)

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extreme f(x,y)=x^2y-15xy^2+12y

extreme points

f (x, y) = x^{2} y - 15 x y^{2} + 12 y

Saddle (- 2, - \frac{4}{15}), Saddle (2, \frac{4}{15})

Solution steps

Find the critical points:

(- 2, - \frac{4}{15}), (2, \frac{4}{15})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 30 x

D (x, y) = - 4 x^{2} + 60 x y - 900 y^{2}

Check the sign of at each critical point

Check critical point

(- 2, - \frac{4}{15}) :

Saddle

Check critical point

(2, \frac{4}{15}) :

Saddle

Saddle (- 2, - \frac{4}{15}), Saddle (2, \frac{4}{15})

f (x, y) = - 2 x^{3} + 6 x y + 3 y^{3}

f (x, y) = x^{2} + 4 y^{2} - 2 x + 8 y - 1

f (x) = x^{2} + 2 x + 3

f (x, y) = 400 - 9 x^{2} - 49 y^{2}

f (x, y) = 3 x^{2} - 12 x + 2 y^{2} - 8 y + 7

What is the extreme f(x,y)=x^2y-15xy^2+12y ?
The extreme f(x,y)=x^2y-15xy^2+12y is Saddle(-2,-4/15),Saddle(2, 4/15)