What is the extreme f(x,y)=3x^2y-y ?

The extreme f(x,y)=3x^2y-y is Saddle(1/(sqrt(3)),0),Saddle(-1/(sqrt(3)),0)

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extreme f(x,y)=3x^2y-y

extreme points

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

Saddle (\frac{1}{3}, 0), Saddle (- \frac{1}{3}, 0)

Solution steps

Find the critical points:

(\frac{1}{3}, 0), (- \frac{1}{3}, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, y) = - 36 x^{2}

Check the sign of at each critical point

Check critical point

(\frac{1}{3}, 0) :

Saddle

Check critical point

(- \frac{1}{3}, 0) :

Saddle

Saddle (\frac{1}{3}, 0), Saddle (- \frac{1}{3}, 0)

f (x, y) = x^{2} + y^{2} + x y + 3 x - 6 y + 1

f (x) = 7 csc (x)

V, V = π r e^{2} \cdot h

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

(2 y^{2} + x^{2}) e^{- (x^{2} + y^{2} - 3)}

What is the extreme f(x,y)=3x^2y-y ?
The extreme f(x,y)=3x^2y-y is Saddle(1/(sqrt(3)),0),Saddle(-1/(sqrt(3)),0)