What is the extreme f(x,y)=(x^2-49)^2+(y^2-9)^2 ?

The extreme f(x,y)=(x^2-49)^2+(y^2-9)^2 is

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Popular Functions >

extreme f(x,y)=(x^2-49)^2+(y^2-9)^2

Solution

extreme

Solution

Maximum (0, 0), Saddle (0, - 3), Saddle (0, 3), Saddle (- 7, 0), Minimum (- 7, - 3), Minimum (- 7, 3), Saddle (7, 0), Minimum (7, - 3), Minimum (7, 3)

Solution steps

Find the critical points:

(0, 0), (0, - 3), (0, 3), (- 7, 0), (- 7, - 3), (- 7, 3), (7, 0), (7, - 3), (7, 3)

\frac{\partial ^{2} f}{\partial x ^{2}} = 12 y^{2} - 36

D (x, y) = (12 y^{2} - 36) (12 x^{2} - 196)

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Check critical point

(0, - 3) :

Saddle

Check critical point

(0, 3) :

Saddle

Check critical point

(- 7, 0) :

Saddle

Check critical point

(- 7, - 3) :

Minimum

Check critical point

(- 7, 3) :

Minimum

Check critical point

(7, 0) :

Saddle

Check critical point

(7, - 3) :

Minimum

Check critical point

(7, 3) :

Minimum

Maximum (0, 0), Saddle (0, - 3), Saddle (0, 3), Saddle (- 7, 0), Minimum (- 7, - 3), Minimum (- 7, 3), Saddle (7, 0), Minimum (7, - 3), Minimum (7, 3)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x,y)=(x^2-49)^2+(y^2-9)^2 ?
The extreme f(x,y)=(x^2-49)^2+(y^2-9)^2 is