Answer by user284331 for $f(x)$ is a bounded polynomial. Prove that $f$ must...
Assume that $f(x)=a_{n}x^{n}+\cdots+a_{1}x+a_{0}$ for $a_{n}\ne 0$ and $n\geq 1$, then...
View ArticleAnswer by Theo Bendit for $f(x)$ is a bounded polynomial. Prove that $f$ must...
If you differentiate $d$ times, you get $d! \cdot b_d$. This is a real number, but remember, it's the only the first derivative that determines increasing or decreasing, not the $d$th derivative! So...
View Article$f(x)$ is a bounded polynomial. Prove that $f$ must be constant.
Question: Suppose $f(x)$ is a bounded polynomial, in other words, there is an $M$ such that $|f(x)|\le M$ for all $x\in R$. Prove that $f$ must be a constant.I think the question assumes $M\in R$. I...
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