What is the extreme (9-x)(9-y)(x+y-9) ?

The extreme (9-x)(9-y)(x+y-9) is Saddle(9,0),Maximum(6,6)

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extreme (9-x)(9-y)(x+y-9)

extreme points

(9 - x) (9 - y) (x + y - 9)

Saddle (9, 0), Maximum (6, 6)

Solution steps

Find the critical points:

(9, 0), (6, 6)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 2 (9 - x)

D (x, y) = - 4 x^{2} + 72 x - 4 x y + 72 y - 4 y^{2} - 405

Check the sign of at each critical point

Check critical point

(9, 0) :

Saddle

Check critical point

(6, 6) :

Maximum

Saddle (9, 0), Maximum (6, 6)

f (x) = - 4 x^{2} - 32 x - 62

f (x, y) = 2 x^{3} + 6 x y^{2} - 3 y^{3} - 150 x

f (x) = - 2 x^{3} - 6 x^{2} + 48 x + 4

f (x) = sin (2 x) - cos (2 x)

(x - 2)^{2} + 1

What is the extreme (9-x)(9-y)(x+y-9) ?
The extreme (9-x)(9-y)(x+y-9) is Saddle(9,0),Maximum(6,6)