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) = 3 x^{2} y - 3 x^{2} - 3 y^{2} + y^{3} + 2

y = x^{3} - 3 x + 7

x^{4} - x^{3} - 6 x^{2}

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

f (x) = \frac{2 x ^{\frac{5}{2}}}{5} - \frac{2 x ^{\frac{3}{2}}}{3} - 6

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)