What is the extreme f(x)=xy^2-8xy ?

The extreme f(x)=xy^2-8xy is Saddle(0,0),Saddle(0,8)

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extreme f(x)=xy^2-8xy

extreme points

f (x) = x y^{2} - 8 x y

Saddle (0, 0), Saddle (0, 8)

Solution steps

Find the critical points:

(0, 0), (0, 8)

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

D (x, y) = - 4 y^{2} + 32 y - 64

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(0, 8) :

Saddle

Saddle (0, 0), Saddle (0, 8)

\frac{5 - x}{2 x + 6}

f (x, y) = \frac{x y}{5 x ^{2} + 2 y ^{2} + 2 x y + 1}

\frac{3 x}{x ^{2} - 9}

f (x, y) = 6 x^{2} - 8 y^{2}

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

What is the extreme f(x)=xy^2-8xy ?
The extreme f(x)=xy^2-8xy is Saddle(0,0),Saddle(0,8)