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 points

f (x, y) = 5 x^{2} y - 3 x y^{2} - x^{2} - y

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)

f (x) = - 3 x^{2} + 10 x - 10

f (x) = 7 sec (x)

f (x) = x^{7} (x + 4)^{4}

f (x) = - x e^{- \frac{x}{2}}

x 36 - x

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…)