What is the extreme f(x)=xy^2-6x^2-3y^2 ?

The extreme f(x)=xy^2-6x^2-3y^2 is Maximum(0,0),Saddle(3,6),Saddle(3,-6)

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extreme f(x)=xy^2-6x^2-3y^2

extreme points

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

Maximum (0, 0), Saddle (3, 6), Saddle (3, - 6)

Solution steps

Find the critical points:

(0, 0), (3, 6), (3, - 6)

\frac{\partial ^{2} f}{\partial x ^{2}} = 2 x - 6

D (x, y) = - 12 (2 x - 6) - 4 y^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Check critical point

(3, 6) :

Saddle

Check critical point

(3, - 6) :

Saddle

Maximum (0, 0), Saddle (3, 6), Saddle (3, - 6)

f (x) = 3 x + \frac{1}{x}

f (x) = x^{3} - 15 x^{2} + 48 x + 2

\frac{x ^{2} - 5}{x + 3}

f (x, y) = x^{2} - x y + y^{2} - 9 x + 6 y + 8

- x^{2} ln (x)

What is the extreme f(x)=xy^2-6x^2-3y^2 ?
The extreme f(x)=xy^2-6x^2-3y^2 is Maximum(0,0),Saddle(3,6),Saddle(3,-6)