What is the extreme f(x)=xy(10-2x-3y) ?

The extreme f(x)=xy(10-2x-3y) is Saddle(0, 10/3),Maximum(5/3 , 10/9)

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extreme f(x)=xy(10-2x-3y)

extreme points

f (x) = x y (10 - 2 x - 3 y)

Saddle (0, \frac{10}{3}), Maximum (\frac{5}{3}, \frac{10}{9})

Solution steps

Find the critical points:

(0, \frac{10}{3}), (\frac{5}{3}, \frac{10}{9})

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

D (x, y) = - 16 x^{2} - 24 x y + 80 x - 36 y^{2} + 120 y - 100

Check the sign of at each critical point

Check critical point

(0, \frac{10}{3}) :

Saddle

Check critical point

(\frac{5}{3}, \frac{10}{9}) :

Maximum

Saddle (0, \frac{10}{3}), Maximum (\frac{5}{3}, \frac{10}{9})

y^{3} + 3 x^{2} y - 6 x^{2} - 6 y^{2} + 2

f (x) = 3000 x^{2} - 2000 x + 8000

f (x) = x^{3} - 5 x^{2} + 6 x

\frac{x}{x ^{2} + 49}

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

What is the extreme f(x)=xy(10-2x-3y) ?
The extreme f(x)=xy(10-2x-3y) is Saddle(0, 10/3),Maximum(5/3 , 10/9)