Mathematics – Classical Analysis and ODEs
Scientific paper
2003-02-18
Mathematics
Classical Analysis and ODEs
7 pages, 3 figures, easy reading for undergraduates, Title changed, some typos fixed
Scientific paper
We call a smooth function of one variable a degree n pseudopolynomial if its n-th derivative has no (real) zeros. An n pseudopolynomial is called hyperbolic if it has exactly n simple zeros. In this short note we describe the necessary and sufficient conditions on the arrangements of 6 points consisting of 3 zeros of pseudopolynomials of degree 3, two zeros of their 1st derivatives and 1 zero of their second derivatives. Besides the standard Rolle's inequalities the restrictions include additional quadratic inequalities of geometric origin. This text is an easy reading accessible for undergraduates. We formulated also two questions not solved yet.
Shapiro Boris
Shapiro Marjorie
No associations
LandOfFree
A few riddles behind Rolle's theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A few riddles behind Rolle's theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A few riddles behind Rolle's theorem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-721769