What is the extreme f(x,y)=2xy-3y-5 ?

The extreme f(x,y)=2xy-3y-5 is Saddle(3/2 ,0)

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extreme f(x,y)=2xy-3y-5

extreme points

f (x, y) = 2 x y - 3 y - 5

Saddle (\frac{3}{2}, 0)

Solution steps

Find the critical points:

(\frac{3}{2}, 0)

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

D (x, y) = - 4

Check the sign of at each critical point

Check critical point

(\frac{3}{2}, 0) :

Saddle

Saddle (\frac{3}{2}, 0)

f (x) = (x - y) (36 - x y)

f (x) = 5 x - 60 x^{\frac{1}{3}}

f (x) = \frac{1}{6} (x^{3} - 6 x^{2} + 9 x + 6)

f (x) = x^{3} + 3 x^{2} - 24 x + 12

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

What is the extreme f(x,y)=2xy-3y-5 ?
The extreme f(x,y)=2xy-3y-5 is Saddle(3/2 ,0)