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Found problems: 26

2015 IMAR Test, 4
(a) Show that, if $I \subset R$ is a closed bounded interval, and $f : I \to R$ is a non-constant monic polynomial function such that $max_{x\in I}|f(x)|< 2$, then there exists a non-constant monic polynomial function $g : I \to R$ such that $max_{x\in I} |g(x)| < 1$. (b) Show that there exists a closed bounded interval $I \subset R$ such that $max_{x\in I}|f(x)| \ge 2$ for every non-constant monic polynomial function $f : I \to R$.
function interval analysis conic real analysis polynomial algebra combinatorics conic sections polynomials