Problem A. 654. (November 2015)
A. 654. Let \(\displaystyle p(x)\) be a polynomial of degree at most \(\displaystyle n\) such that \(\displaystyle \big|p(x)\big|\le\frac{1}{\sqrt{x}}\) for \(\displaystyle 0<x\le 1\). Prove that \(\displaystyle \big|p(0)\big|\le 2n+1\).
(5 pont)
Deadline expired on December 10, 2015.
Statistics:
5 students sent a solution. 5 points: Bukva Balázs, Williams Kada. 3 points: 1 student. 2 points: 1 student. 0 point: 1 student.
Problems in Mathematics of KöMaL, November 2015