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

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

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

extreme points

f (x) = 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^{3} - 9 x^{2} + 15 x + 3

f (x, y) = 2 x^{3} - y^{2} - 6 x y + 23

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

f (x) = 2 x^{3} + 3 x^{2} - 12 x - 18

f (x, y) = 2 x y + \frac{1}{x} + \frac{4}{y}

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