query: If for each $x$ there is $n_x$ such that $f^{(n_x)}(x)=0,$ then $f$ is a polynomial.
positive_passages.docid: 148813
positive_passages.text: Prove: $f: \mathbb{R} \rightarrow \mathbb{R}$ st for every $x \in \mathbb{R}$ there exists $n$ st $f^{(n)}(x) = 0$, f is a polynomial.
negative_passages.docid: 155444
negative_passages.text: Show that entire function $f$ is a polynomial of degree at most $n$
negative_passages.docid: 124380
negative_passages.text: existence of sequence of polynomial
negative_passages.docid: 41810
negative_passages.text: Should all polynomial functions from F to F (F is a field) have coefficients in F?
negative_passages.docid: 6484
negative_passages.text: Polynomials in one variable with infinitely many roots.
negative_passages.docid: 138054
negative_passages.text: Proving that $\int_0^1 f(x)e^{nx}\,{\rm d}x = 0$ for all $n\in\mathbb{N}_0$ implies $f(x) = 0$
negative_passages.docid: 33011
negative_passages.text: Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
negative_passages.docid: 40014
negative_passages.text: A polynomial that is zero on an open set
negative_passages.docid: 148410
negative_passages.text: How do I show $f_n(x)=n^2 x^n(1-x)$ pointwise converges to $0$ on $[0,1]$?
negative_passages.docid: 54875
negative_passages.text: How to prove polynomials with degree $n$ does not form a vector space?
negative_passages.docid: 97729
negative_passages.text: Show that a polynomial $f(x)$ over a field $k$ is irreducible if and only if the polynomial $f(x+1)$ is irreducible
negative_passages.docid: 108264
negative_passages.text: A polynomial is called a Fermat's polynomial...
negative_passages.docid: 154507
negative_passages.text: If all the roots of a polynomial P(z) have negative real parts, prove that all the roots of P'(z) also have negative real parts
negative_passages.docid: 127547
negative_passages.text: Prove that If $f$ is polynomial function of even degree $n$ with always $f\geq0$ then $f+f'+f''+\cdots+f^{(n)}\geq 0$.
negative_passages.docid: 109721
negative_passages.text: The number of zeros in a polynomial
negative_passages.docid: 114146
negative_passages.text: Polynomial in $n$ variables
negative_passages.docid: 71071
negative_passages.text: Nonzero $f \in C([0, 1])$ for which $\int_0^1 f(x)x^n dx = 0$ for all $n$