What is the extreme f(x,y)=(7-x)(7-y)(x+y-7) ?

The extreme f(x,y)=(7-x)(7-y)(x+y-7) is Saddle(7,0),Maximum(14/3 , 14/3)

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extreme f(x,y)=(7-x)(7-y)(x+y-7)

extreme points

f (x, y) = (7 - x) (7 - y) (x + y - 7)

Saddle (7, 0), Maximum (\frac{14}{3}, \frac{14}{3})

Solution steps

Find the critical points:

(7, 0), (\frac{14}{3}, \frac{14}{3})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 2 (7 - x)

D (x, y) = - 4 x^{2} + 56 x - 4 x y + 56 y - 4 y^{2} - 245

Check the sign of at each critical point

Check critical point

(7, 0) :

Saddle

Check critical point

(\frac{14}{3}, \frac{14}{3}) :

Maximum

Saddle (7, 0), Maximum (\frac{14}{3}, \frac{14}{3})

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

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

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

P (x, y) = 12 x^{6} - 7 x^{3} y - 10 y^{2}

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

What is the extreme f(x,y)=(7-x)(7-y)(x+y-7) ?
The extreme f(x,y)=(7-x)(7-y)(x+y-7) is Saddle(7,0),Maximum(14/3 , 14/3)