Recent content by olast1

Let me rephrase, what I am having a problem with at this point is to relate the (B1,...,Bn-1) in my definition of P'(x) with the (C1,...,Cn-1) if I write P'(x) in the usual manner P'(x)=sum(i=1,...,n-1){Ci*x^i} Then obviously I can easily relate the Ci to your Ai.

Well, what I am having problems with is to find a formula to relate the (B1,...,Bn-1) in my equation of P'(x) to your (a1,...an).

I am not sure I understand what you are getting at. I do not know if it helps or overlap with what you are saying but here is what I tried to do at this point: if P(x) is a polynomial of degree n, then its derivative P'(x) is a polynomial of degree n-1. Therefore, I have tried to...

Thank you for your suggestion. Sturm's theorem is something I could use. However, I am not sure how I can use it to find constraints on the coefficients that guarantee the monotonicity of the polynomial over [0,1].

Yes, it is a Math class which is part of the first year in the master program in economics. Although I am not sure how, I hope this helps.

Master Level.

Thank you for your answer, but I am not sure I understand what you mean. Can you explain?

What general constraints on the coefficients of a polynomial of degree n do I need to impose to guarantee that this polynomial is strictly increasing on [0,1]?