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

The extreme f(x,y)=3xy-6x-y^2 is Saddle(4/3 ,2)

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

extreme points

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

Saddle (\frac{4}{3}, 2)

Solution steps

Find the critical points:

(\frac{4}{3}, 2)

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

D (x, y) = - 9

Check the sign of at each critical point

Check critical point

(\frac{4}{3}, 2) :

Saddle

Saddle (\frac{4}{3}, 2)

f (x) = \frac{8}{x ^{2} + 1}

f (2.52, 5.15) = 3 x^{4} y^{2} - 18 x y

f (x) = - 3 x^{4} + 20 x^{3} - 36 x^{2} + 7

y = - 2 + 5 sin (\frac{π}{12} (x - 2))

(x^{2} - 1) (x^{2} - 9)

What is the extreme f(x,y)=3xy-6x-y^2 ?
The extreme f(x,y)=3xy-6x-y^2 is Saddle(4/3 ,2)