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Dual Smale’s mean value conjecture
Aimo Hinkkanen, Ilgiz Kayumov, Diana Khammatova
Source abstract
We prove the dual Smale’s mean value conjecture for polynomials of degree six: if f f is a polynomial of degree six with f ( 0 ) = 0 f(0)=0 and f ′ ( 0 ) = 1 f’(0)=1 , then there is a point ζ \zeta such that f ′ ( ζ ) = 0 f’(\zeta )=0 and | f ( ζ ) / ζ | ≥ 1 / 6 | f(\zeta )/\zeta | \geq 1/6 .
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