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April 2nd, 2009, 06:28 PM   #1
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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?
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April 3rd, 2009, 06:24 PM   #2
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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.
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April 3rd, 2009, 08:04 PM   #3
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Re: Critical points

Thanks for the help and clearing that up for me, much appreciated!
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