November 3rd, 2012, 11:23 AM  #1 
Newbie Joined: Sep 2012 Posts: 22 Thanks: 0  Second Derivative Test
When do you use the second derivative test instead of the first derivative test when determining relative max/min?

November 3rd, 2012, 11:33 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Second Derivative Test
You can use either the first derivative test or the second derivative test to determine the nature of extrema. Which you use is often a matter of convenience, i.e., which is simpler.

November 3rd, 2012, 11:40 AM  #3 
Newbie Joined: Sep 2012 Posts: 22 Thanks: 0  Re: Second Derivative Test
That's what I thought because I used both for the same problem and got the same answer. So there's no situation where you'd have to use one over the other unless specific in the question? Excluding, when using the second derivative and getting 0 as an answer, because I know when that happens you have to use the FDT. Thank you very much!

November 3rd, 2012, 12:05 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Second Derivative Test
When both the first and second derivatives are zero at a point, then it is not an extremum. Sometimes it is easier to use one test over the other, and unless otherwise instructed I would use the easier of the two tests.


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