What is the extreme f(x,y)=-x^2+5y^2+10x-10y-28 ?

The extreme f(x,y)=-x^2+5y^2+10x-10y-28 is Saddle(5,1)

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extreme f(x,y)=-x^2+5y^2+10x-10y-28

extreme points

f (x, y) = - x^{2} + 5 y^{2} + 10 x - 10 y - 28

Saddle (5, 1)

Solution steps

Find the critical points:

(5, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 10

D (x, y) = - 20

Check the sign of at each critical point

Check critical point

(5, 1) :

Saddle

Saddle (5, 1)

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

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

f (x) = 120 x - 0.4 x^{4} + 1000

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

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

What is the extreme f(x,y)=-x^2+5y^2+10x-10y-28 ?
The extreme f(x,y)=-x^2+5y^2+10x-10y-28 is Saddle(5,1)