January 23rd, 2012, 03:27 PM  #1 
Newbie Joined: Jan 2012 Posts: 1 Thanks: 0  Classes of equations?
How do I find a complete set of equations, or classes of equations, that satisfy the following conditions: The function must be smooth and connected everywhere. When the function crosses the yaxis it must have a finite negative value (let us call the absolute value of this value a), and the slope of the function where it crosses the yaxis must be zero. At some finite positive xvalue (let's call this value b) the function must cross the xaxis. At point b the slope must be infinite, and b must be an inflection point. Finally, the graph should be symmetric about the yaxis. I know that the following equation satisfies all but the last of these conditions, but I do not know how to identify the class of equations that satisfy them all. y = (xa)^(1/b) Can anyone help? 
January 27th, 2012, 12:50 AM  #2 
Senior Member Joined: Oct 2008 Posts: 215 Thanks: 0  Re: Classes of equations?
This is not linear algebra problem. You could have a try to the function with period 2 and it is sqrt(1x^2) when 1<=x<=1 
January 27th, 2012, 12:54 AM  #3 
Senior Member Joined: Oct 2008 Posts: 215 Thanks: 0  Re: Classes of equations?
It should be function with period 4 and sqrt(1x^2) when 1<=x<=1 and sqrt(1(x2)^2) when 1<=x<=3 

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