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May 23rd, 2010, 03:50 AM  #1 
Newbie Joined: Apr 2010 Posts: 12 Thanks: 0  Second Derivative Test
Let f(x) = (1 + x)^x Use the Second Derivative Test to determine whether f has a local maximum or a local minimum at x = 0. This question has gave me such a headache, as working out f''(x), is extremely long and I am thinking that there has to be some simple way to do it? 
May 23rd, 2010, 07:07 AM  #2 
Senior Member Joined: Nov 2008 Posts: 265 Thanks: 0  Re: Second Derivative Test
I believe the first derivative is Second derivative: Sorry the exponents look weird, don't know how to use latex that well. They should be (x1) or (x2) Or I guess you could use logarithmic differentiation. 
May 23rd, 2010, 07:24 AM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,599 Thanks: 941 Math Focus: Elementary mathematics and beyond  Re: Second Derivative Test 
May 23rd, 2010, 07:50 AM  #4  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,599 Thanks: 941 Math Focus: Elementary mathematics and beyond  Re: Second Derivative Test Quote:
 
May 23rd, 2010, 08:19 AM  #5 
Senior Member Joined: Nov 2008 Posts: 265 Thanks: 0  Re: Second Derivative Test
Oh, thanks a lot greg1313. I had a feeling logarithmic differentiation would be more useful in this case. 
May 26th, 2010, 04:28 AM  #6 
Newbie Joined: May 2010 Posts: 1 Thanks: 0  Re: Second Derivative Test
there is first derivative test also


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