What is the extreme f(x,y)=-6x^2+5y^2+12x-20y-18 ?

The extreme f(x,y)=-6x^2+5y^2+12x-20y-18 is Saddle(1,2)

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extreme f(x,y)=-6x^2+5y^2+12x-20y-18

extreme points

f (x, y) = - 6 x^{2} + 5 y^{2} + 12 x - 20 y - 18

Saddle (1, 2)

Solution steps

Find the critical points:

(1, 2)

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

D (x, y) = - 120

Check the sign of at each critical point

Check critical point

(1, 2) :

Saddle

Saddle (1, 2)

x - x

f (t) = 135 t - 5 t^{3}, - 4 \leq t \leq \infty

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

P (x, y) = 2 x + y

y = \frac{5280}{π x ^{2}} - \frac{4}{3} x

What is the extreme f(x,y)=-6x^2+5y^2+12x-20y-18 ?
The extreme f(x,y)=-6x^2+5y^2+12x-20y-18 is Saddle(1,2)