Suppose f(x) is a polynomial with real coefficient and $f(x)>=0$ $x \in R$ let $g(x)=f(x)+f^{'}(x) +f^{"}(x)+..$. prove that $g(x)>=0 for all x\in R$
1519
Sum of derivatives of a polynomial
83291
Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
30860
Prove that $f(x)=0$ in $[-1,1]$.
57193
Prove that $f$ has derivatives of all orders at $x=0$, and that $f^{(n)}(0)=0$ for $n=1,2,3\ldots$
139019
Polynomial satisfying $f(x) = f'(x) \cdot f''(x)$
144589
Proving that if $f(x) \le g(x)$ then $f(x_0) \le g(x_0)$
28007
Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $
117099
Coefficient Problem (polynomial expansion)
140817
Real Analysis Inequality Proof Involving Reals and Rationals $0 < |r - q| < \varepsilon$
95684
Show that $g'(x)+g(x)-2e^x=0$
26219
Suppose f is a function such that f'(x) = 1/x for all x > 0. Prove that if f(1) = 0, then f(xy) = f(x) + f(y) for all x,y > 0
103340
Show that this entire function is polynomial.
65619
Does $f^{(n)} = 0$ imply that complex $f$ is a polynomial?
155575
Proving a polynomial $f(x)$ composite for infinitely many $x$
137218
Does there exist a polynomial $f(x)$ with real coefficients such that $f(x)^2$ has fewer nonzero coefficients than $f(x)$?
101918
Let $f(x)=ax^2+bx+c$ where $a,b,c$ are real numbers. Suppose $f(-1),f(0),f(1) \in [-1,1]$. Prove that $|f(x)|\le \frac{3}{2}$ for all $x \in [-1,1]$.
107795
If $\,f''(x) \ge f(x)$, for all $x\in[0,\infty),$ and $\,f(0)=f'(0)=1$, then is $\,f(x)>0$?