July 28th, 2012, 08:42 PM  #1 
Newbie Joined: Feb 2012 Posts: 19 Thanks: 0  Can anyone prove this?
We know: (1) f(x)/x is strictly decreasing in x; (2) f(0)=0 and f(3)=0; (3) f(x) is continuous in x; Can we prove that f(x) is concave in x on [0, 3]? Or f(x) is singlepeaked on [0, 3]? Thanks. 
July 29th, 2012, 01:23 PM  #2 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: Can anyone prove this? [color=#000000]No, take as a counter example.[/color] 
July 29th, 2012, 01:40 PM  #3 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Can anyone prove this?
Surely, is not "strictly decreasing"?

July 30th, 2012, 12:04 AM  #4  
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: Can anyone prove this? Quote:
 

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