May 20th, 2012, 02:31 AM  #1 
Senior Member Joined: Apr 2012 Posts: 135 Thanks: 1  differentiability
1) What happens if a function has a jump discontinuity but the left and right side of the derivative are equal? 2) What happens if a function has no critical points or the derivative has complex roots for e.g. f(x)=x^4+x^2+x+1 => f'(x)=4x^3+2x+1? 
May 20th, 2012, 05:56 AM  #2  
Senior Member Joined: Jun 2011 Posts: 298 Thanks: 0  Re: differentiability Quote:
Quote:
on  
May 20th, 2012, 12:10 PM  #3  
Senior Member Joined: Jun 2011 Posts: 298 Thanks: 0  Re: differentiability Quote:
Consider on bothsides of 0. The and There is a jump of 2 units from the left hand side to the right hand side. Since does not exist, it's discontinuous apart from the jump. exists in and Quote:
 
May 20th, 2012, 01:23 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond  Re: differentiability
I've deleted the post. Thanks for the correction. 

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