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

The extreme f(x,y)=xy^2-x^2y-3xy is Saddle(0,3),Maximum(-1,1)

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

extreme points

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

Saddle (0, 3), Maximum (- 1, 1)

Solution steps

Find the critical points:

(0, 3), (- 1, 1)

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

D (x, y) = 4 x y - 4 x^{2} - 12 x - 4 y^{2} + 12 y - 9

Check the sign of at each critical point

Check critical point

(0, 3) :

Saddle

Check critical point

(- 1, 1) :

Maximum

Saddle (0, 3), Maximum (- 1, 1)

f (x) = x^{4} - 6 x^{2}, 0 \leq x \leq 3

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

V, V = 31 π r 2 h

f (x) = x^{3} - 3 x^{2} - 45 x + 9

f (x) = 4 x^{2} - 2 x

What is the extreme f(x,y)=xy^2-x^2y-3xy ?
The extreme f(x,y)=xy^2-x^2y-3xy is Saddle(0,3),Maximum(-1,1)