What is the extreme f(x,y)=3x-2y+6xy ?

The extreme f(x,y)=3x-2y+6xy is Saddle(1/3 ,-1/2)

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extreme f(x,y)=3x-2y+6xy

extreme points

f (x, y) = 3 x - 2 y + 6 x y

Saddle (\frac{1}{3}, - \frac{1}{2})

Solution steps

Find the critical points:

(\frac{1}{3}, - \frac{1}{2})

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

D (x, y) = - 36

Check the sign of at each critical point

Check critical point

(\frac{1}{3}, - \frac{1}{2}) :

Saddle

Saddle (\frac{1}{3}, - \frac{1}{2})

f (x) = - 2 x^{3} + 6 x - 1

f (x) = - 3 x^{6} ln (2 x)

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

f (x) = x (x + 4)

f (x) = (x^{2} - 1)^{3}, - 1 \leq x \leq 3

What is the extreme f(x,y)=3x-2y+6xy ?
The extreme f(x,y)=3x-2y+6xy is Saddle(1/3 ,-1/2)