What is the extreme f(x,y)=5x^2y-3xy^2-x^2-y ?

The extreme f(x,y)=5x^2y-3xy^2-x^2-y is Saddle(0.60235…,0.22527…),Saddle(-0.35469…,0.17430…)

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extreme f(x,y)=5x^2y-3xy^2-x^2-y

extreme

Saddle (0.60235 \dots, 0.22527 \dots), Saddle (- 0.35469 \dots, 0.17430 \dots)

Solution steps

Find the critical points:

(0.60235 \dots, 0.22527 \dots), (- 0.35469 \dots, 0.17430 \dots)

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

D (x, y) = - 100 x^{2} + 60 x y + 12 x - 36 y^{2}

Check the sign of at each critical point

Check critical point

(0.60235 \dots, 0.22527 \dots) :

Saddle

Check critical point

(- 0.35469 \dots, 0.17430 \dots) :

Saddle

Saddle (0.60235 \dots, 0.22527 \dots), Saddle (- 0.35469 \dots, 0.17430 \dots)

What is the extreme f(x,y)=5x^2y-3xy^2-x^2-y ?
The extreme f(x,y)=5x^2y-3xy^2-x^2-y is Saddle(0.60235…,0.22527…),Saddle(-0.35469…,0.17430…)