What is the extreme f(x,y)=xy(1-10x-y) ?

The extreme f(x,y)=xy(1-10x-y) is Saddle(0,1),Maximum(1/30 , 1/3)

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extreme f(x,y)=xy(1-10x-y)

extreme points

f (x, y) = x y (1 - 10 x - y)

Saddle (0, 1), Maximum (\frac{1}{30}, \frac{1}{3})

Solution steps

Find the critical points:

(0, 1), (\frac{1}{30}, \frac{1}{3})

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

D (x, y) = - 400 x^{2} - 40 x y + 40 x - 4 y^{2} + 4 y - 1

Check the sign of at each critical point

Check critical point

(0, 1) :

Saddle

Check critical point

(\frac{1}{30}, \frac{1}{3}) :

Maximum

Saddle (0, 1), Maximum (\frac{1}{30}, \frac{1}{3})

f (x, y) = 9 - 3 y^{2} + 6 x^{2} - 2 y - 3 x^{3}

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

f (x, y, λ) = 9 - x^{2} - y^{2} + λ (4 - x - y)

\frac{1 - x}{x ^{2} + 3}

g (t) = u^{1} (t) + 2 u^{3} (t) - 6 u^{4} (t)

What is the extreme f(x,y)=xy(1-10x-y) ?
The extreme f(x,y)=xy(1-10x-y) is Saddle(0,1),Maximum(1/30 , 1/3)