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March 29th, 2012, 12:01 PM   #1
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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
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March 29th, 2012, 12:10 PM   #2
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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.
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March 29th, 2012, 12:27 PM   #3
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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 x-axis on (1,3), with a point of inflection at x = 4, then approaching the x-axis 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 x-axis for all x in the domain:

[attachment=0:lvvr4bhc]graph01.jpg[/attachment:lvvr4bhc]
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