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

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

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

extreme points

f (x, y) = 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})

P (b, s) = b + 2 s

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

x^{\frac{2}{3}} (\frac{5}{2} - x)

f (x) = 2 x^{5} + 5 x^{4}

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

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