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March 18th, 2009, 12:53 PM  #1 
Member Joined: Mar 2009 From: San Bernardino, California Posts: 50 Thanks: 0  Quick Second Partial Derivative Test Question
I understand that when the discriminant of a function defined as is less than zero at point (a,b) then the function has a saddle point at (a,b) and if the discriminant is greater than zero at (a,b) there exists a local extrema at point (a,b) (D=0 is inconclusive). Also if there is a local extrema then: there exists a local minimum at (a,b) there exists a local maximum at (a,b) However what about the case that D>0 at (a,b) indicating that there is a local extrema, but ? This can't be a saddle point can it? Or does the test fail? 
March 18th, 2009, 11:38 PM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: Quick Second Partial Derivative Test Question
In that case look at instead. Also: the singular is extremum, the plural is extrema. 
March 19th, 2009, 07:51 PM  #3 
Member Joined: Mar 2009 From: San Bernardino, California Posts: 50 Thanks: 0  Re: Quick Second Partial Derivative Test Question
Ahh ok thank you. Is there any particular reason we choose to evaluate first rather than ?

March 19th, 2009, 09:21 PM  #4 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: Quick Second Partial Derivative Test Question
No. You can check any directional derivative.


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