April 2nd, 2009, 06:28 PM  #1 
Newbie Joined: Mar 2009 Posts: 6 Thanks: 0  Critical points
p(x)= x^3  ax^2 + x where a is a positive constant, is what is being looked at and the questions I have are; 1.) What values of A does the graph of p(x) have no critical points? 2.) What values of A does the graph of p(x) have two critical points? 
April 3rd, 2009, 06:24 PM  #2 
Member Joined: Feb 2008 Posts: 89 Thanks: 0  Re: Critical points
Greetings: The critrical values are those real values of x for which P'(x) = 0. The derivative is quadratic and hence P has no c.p.s when its discriminant is negative. That said, letting D be said discriminant, solve for a in the inequality D < 0. Similarly, P has two distinct c.p.s when D > 0. Regards, Rich B. 
April 3rd, 2009, 08:04 PM  #3 
Newbie Joined: Mar 2009 Posts: 6 Thanks: 0  Re: Critical points
Thanks for the help and clearing that up for me, much appreciated!


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