What is the extreme f(x,y)=x^{10}-y^{10}-10x+10y-1 ?

The extreme f(x,y)=x^{10}-y^{10}-10x+10y-1 is Saddle(1,1)

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extreme f(x,y)=x^{10}-y^{10}-10x+10y-1

extreme points

f (x, y) = x^{10} - y^{10} - 10 x + 10 y - 1

Saddle (1, 1)

Solution steps

Find the critical points:

(1, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 90 y^{8}

D (x, y) = - 8100 x^{8} y^{8}

Check the sign of at each critical point

Check critical point

(1, 1) :

Saddle

Saddle (1, 1)

y = x^{3} - 3 x^{2} + 4

f (x) = 1 - 2 x^{2}

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

f (x) = 1 - x^{3}

- 14 - x

What is the extreme f(x,y)=x^{10}-y^{10}-10x+10y-1 ?
The extreme f(x,y)=x^{10}-y^{10}-10x+10y-1 is Saddle(1,1)