What is the extreme f(x,y)=3x^2y+4xy-2 ?

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

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extreme f(x,y)=3x^2y+4xy-2

extreme points

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

Saddle (0, 0), Saddle (- \frac{4}{3}, 0)

Solution steps

Find the critical points:

(0, 0), (- \frac{4}{3}, 0)

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

D (x, y) = - 36 x^{2} - 48 x - 16

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(- \frac{4}{3}, 0) :

Saddle

Saddle (0, 0), Saddle (- \frac{4}{3}, 0)

\frac{1}{2} (5 x - 3)

f (x) = (3 x^{2} + 6)^{2}

f (x, y) = x^{2} + 4 x y + 5 y^{2} - 7 x + 9 y - 10

f (x) = 9 x - 18 cos (x), - 2 \leq x \leq 0

f (x) = 2 x^{2} - 4 x, 0 \leq x \leq 3

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