# Solution: 2017-14 Polynomials of degree at most n

Let $$f(x)\in \mathbb R[x]$$ be a polynomial of degree at most $$n$$ such that $x^2+f(x)^2\le 1$ for all $$-1\le x\le 1$$. Prove that $$\lvert f'(x)\rvert \le 2(n-1)$$ for all $$-1\le x\le 1$$.

The best solution was submitted by Huy Tùng Nguyễn (수리과학과 2016학번). Congratulations!

Here is his solution of problem 2017-14.

Alternative solutions were submitted by 유찬진 (수리과학과 2015학번, +3), 이본우 (2017학번, +2). One incorrect solution was submitted.

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