What is the extreme g(x,y)=xy+(y+x)(10-x-y) ?

The extreme g(x,y)=xy+(y+x)(10-x-y) is Maximum(10/3 , 10/3)

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extreme g(x,y)=xy+(y+x)(10-x-y)

extreme points

g (x, y) = x y + (y + x) (10 - x - y)

Maximum (\frac{10}{3}, \frac{10}{3})

Solution steps

Find the critical points:

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

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

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

Maximum

Maximum (\frac{10}{3}, \frac{10}{3})

f (x, y) = x^{2} - y^{2} + 6 x - 8 y + 25

f (x, y) = x + 4 y

f (x) = 6 + (7 + 5 x)^{\frac{2}{5}}

y = x e^{- x}

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

What is the extreme g(x,y)=xy+(y+x)(10-x-y) ?
The extreme g(x,y)=xy+(y+x)(10-x-y) is Maximum(10/3 , 10/3)