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

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

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

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = - 144

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = 120 x - x^{2} - (950 + 14 x)

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

f (x) = \frac{x ^{3}}{3} - 3 x^{2} + 8 x - 4

f (x) = x^{4} + \frac{4}{3 x ^{3}}

f (x) = 3 x^{2} - 18 x + 5

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