What is the extreme f(x,y)=7-xy+x^5y^3 ?

The extreme f(x,y)=7-xy+x^5y^3 is Saddle(0,0),Saddle(0,0),Saddle(0,0)

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extreme f(x,y)=7-xy+x^5y^3

extreme points

f (x, y) = 7 - x y + x^{5} y^{3}

Saddle (0, 0), Saddle (0, 0), Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0), (0, 0), (0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 6 x^{5} y

D (x, y) = - 105 x^{8} y^{4} + 30 x^{4} y^{2} - 1

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(0, 0) :

Saddle

Check critical point

(0, 0) :

Saddle

Saddle (0, 0), Saddle (0, 0), Saddle (0, 0)

f (x) = 2 x^{3} - 3 x^{2} - 12 x + 8

f (x) = 3 x^{2} - x^{3}, 1 \leq x \leq 5

f (x, y) = x^{2} + y^{3} - 4 x - 3 y

f (x) = cos (3 x) - 2

f (x) = - sin (x) - 4

What is the extreme f(x,y)=7-xy+x^5y^3 ?
The extreme f(x,y)=7-xy+x^5y^3 is Saddle(0,0),Saddle(0,0),Saddle(0,0)