What is the extreme f(x)=(x^2-6x)(y^2-7y) ?

The extreme f(x)=(x^2-6x)(y^2-7y) is Saddle(0,7),Saddle(6,7),Saddle(0,0),Saddle(6,0),Maximum(3, 7/2)

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extreme f(x)=(x^2-6x)(y^2-7y)

extreme points

f (x) = (x^{2} - 6 x) (y^{2} - 7 y)

Saddle (0, 7), Saddle (6, 7), Saddle (0, 0), Saddle (6, 0), Maximum (3, \frac{7}{2})

Solution steps

Find the critical points:

(0, 7), (6, 7), (0, 0), (6, 0), (3, \frac{7}{2})

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

D (x, y) = - 12 x^{2} y^{2} + 84 x^{2} y - 196 x^{2} + 72 x y^{2} - 504 x y + 1176 x - 144 y^{2} + 1008 y - 1764

Check the sign of at each critical point

Check critical point

(0, 7) :

Saddle

Check critical point

(6, 7) :

Saddle

Check critical point

(0, 0) :

Saddle

Check critical point

(6, 0) :

Saddle

Check critical point

(3, \frac{7}{2}) :

Maximum

Saddle (0, 7), Saddle (6, 7), Saddle (0, 0), Saddle (6, 0), Maximum (3, \frac{7}{2})

f (x) = - 5 sec (x)

f (x) = (1)^{3 n}

\frac{2 x + 1}{3 x ^{2} - 39 x + 108}

y = 2 x^{2} + 8 x - 1

x^{\frac{2}{3}} (x - 4)

What is the extreme f(x)=(x^2-6x)(y^2-7y) ?
The extreme f(x)=(x^2-6x)(y^2-7y) is Saddle(0,7),Saddle(6,7),Saddle(0,0),Saddle(6,0),Maximum(3, 7/2)