What is the extreme f(x)=-2x^2+3xy-9x ?

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

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extreme f(x)=-2x^2+3xy-9x

extreme points

f (x) = - 2 x^{2} + 3 x y - 9 x

Saddle (0, 3)

Solution steps

Find the critical points:

(0, 3)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, y) = - 9

Check the sign of at each critical point

Check critical point

(0, 3) :

Saddle

Saddle (0, 3)

f (x) = 36 - t^{2}

- x^{3} + 2 x^{2} + 4 x + 7

f (x) = 2 x^{3} - 39 x^{2} + 180 x + 1

y = 6 x - 12

1353.0186700000000 \dots

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