What is the extreme f(x,y)=xy(30-x-y) ?

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

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extreme f(x,y)=xy(30-x-y)

extreme points

f (x, y) = x y (30 - x - y)

Saddle (0, 30), Maximum (10, 10)

Solution steps

Find the critical points:

(0, 30), (10, 10)

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

D (x, y) = - 4 x y + 120 x - 4 x^{2} + 120 y - 4 y^{2} - 900

Check the sign of at each critical point

Check critical point

(0, 30) :

Saddle

Check critical point

(10, 10) :

Maximum

Saddle (0, 30), Maximum (10, 10)

y = \frac{5 x}{x ^{2} - 1}

x^{2} - 9 x + 5

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

f (x) = 12 y - 64

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

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