Dual Smale's mean value conjecture

Abstract

© 2019 American Mathematical Society. We prove the dual Smale's mean value conjecture for polynomials of degree six: if f is a polynomial of degree six with f(0) = 0 and f′(0) = 1, then there is a point ζ such that f′(ζ) = 0 and |f(ζ)/ζ| ≥ 1/6.