What is the extreme x^2y-15xy^2+12y ?

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

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extreme x^2y-15xy^2+12y

extreme points

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) = x^{4} + x^{3} - 9

f (x, y) = x^{3} + y^{3} - 30 x y

f (x) = - x^{2} + 8 x - 2

f (x) = - x^{3} + 3 x + 1

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

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