March 29th, 2012, 12:01 PM  #1 
Member Joined: Feb 2012 Posts: 42 Thanks: 0  graph based on conditions
Hello, I have created a graph based on the following conditions. I am just learning this subject, so could someone please tell me if I have this correct ? Thanks kindly domain g=(0,infinity) limit as x tends to 0 g(x)= negative infinity limit as x tends to infinity g(x) = 0 g'(1) = 0 g'(3) = 0 g'(x) < 0 if 1<x<3 g''(x) < 0 if x<2 or x>4 g''(x) > 0 if 2<x<4 
March 29th, 2012, 12:10 PM  #2 
Senior Member Joined: Feb 2012 Posts: 628 Thanks: 1  Re: graph based on conditions
That graph would not satisfy those conditions, although it's close. In order for the function g(x) to be concave and approach 0 as x goes to infinity, it has to be negative and increasing past x=4.

March 29th, 2012, 12:27 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: graph based on conditions
You are close. You concavity is wrong...you have a point of inflection to the right of x = 4, and g''(x) > 0 to the right of that, but we need g''(x) < 0 for all x greater than 4. You will need the graph of g(x) to go below the xaxis on (1,3), with a point of inflection at x = 4, then approaching the xaxis from below so that concavity can be down as it approaches its asymptote. You will also avoid the unnecessary local max to the right of x = 4 as well. You could also avoid this problem by keeping the graph below the xaxis for all x in the domain: [attachment=0:lvvr4bhc]graph01.jpg[/attachment:lvvr4bhc] 

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