What is the extreme f(x)=x^2-6x+9-4y^2 ?

The extreme f(x)=x^2-6x+9-4y^2 is Saddle(3,0)

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extreme f(x)=x^2-6x+9-4y^2

extreme points

f (x) = x^{2} - 6 x + 9 - 4 y^{2}

Saddle (3, 0)

Solution steps

Find the critical points:

(3, 0)

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

D (x, y) = - 16

Check the sign of at each critical point

Check critical point

(3, 0) :

Saddle

Saddle (3, 0)

f (x) = x^{\frac{8}{7}} + 8 x^{\frac{1}{7}}

f (x) = \frac{x}{x - 6}

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

f (x, y) = x^{2} + y^{2} + 8 x - 12 y - 9

f (x, y) = 2 x y + 3 x + 4 y

What is the extreme f(x)=x^2-6x+9-4y^2 ?
The extreme f(x)=x^2-6x+9-4y^2 is Saddle(3,0)