Distinguishing Max, Min & Saddle - Choosing Coordinate Systems

[MarianaA]

Hi every one, I have two questions, I hope some one can help me.
Thanks.

How can I distinguish between a maximum, minimum or a saddle?

When are times when a particular coordinate system is a better choice the n the other two (rectangular, cylindrical and spherical)?

 

[EnumaElish]

How can I distinguish between a maximum, minimum or a saddle?

You could start by writing out the definition for each.

 

[MarianaA]

but I don't know the definition

 

[DeadWolfe]

A minimum occurs when the Hessian is positive definite, a maximum when it is negative definite, and a saddle point when the Hessian has positive and negative eigenvalues.

 

[MarianaA]

Thanks ^_^
How about my second question:

When are times when a particular coordinate system is a better choice the n the other two (rectangular, cylindrical and spherical)?

 

[EnumaElish]

Cylindrical coordinates are useful in analyzing systems that are symmetrical about an axis. For example the infinitely long cylinder that has the Cartesian equation x² + y² = c² has the very simple equation r = c in cylindrical coordinates.

By extension, one can say that spherical coordinates are useful in analyzing systems that are symmetrical about point.

For everything else, there are rectangular coordinates.

 

[EnumaElish]

I am assuming this is not homework. If it is, this thread will probably be deleted.

 

[MarianaA]

Well I need to know this so I can do my homework
Thanks ^_^