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

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

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

extreme points

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

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

Solution steps

Find the critical points:

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

\frac{\partial ^{2} f}{\partial x ^{2}} = - 6 x

D (x, y) = - 36 y^{2} + 24 y - 4

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

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

Saddle

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

f (x) = 7 x + 9, - 6 \leq x \leq 3

\frac{2 x}{( 3 x - 6 )}

f (x) = - x^{3} + x^{2} + 4 x - 1

f (x) = 2 (3 x)^{x}, 0.1 \leq x \leq 1

f (x) = 8 x - 9 sin (x), 0 \leq x \leq \frac{π}{2}

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