If $f \neq 0$ there exist $x_0$ with $|f(x_0)| < |f'(x_0)|$
30860
Prove that $f(x)=0$ in $[-1,1]$.
84313
$|f(z)|\le 1-|z|\forall z\in D$, we need to show $f\equiv 0$
148585
Show that, for any $\epsilon>0$, there exist two rationals such that $q < x < q'$ and $|q-q'|<\epsilon$
105316
Prove : $|x - y| \leqslant \epsilon$ $\forall \epsilon > 0$ iff $x = y$
112409
If $f$ is continuous and $f'(x)\ge 0$, outside of a countable set, then $f$ is increasing
76790
Condition to guarantee $f=0$ on $[a,b]$
45885
If there exist sequence such that $g(x_n)=f(x_{n+1})$, then we have $g(x_0)=f(x_0)$ for some $x_0$
111076
If $f$ is non-constant and entire, prove that there exists a $z_0 \in C$ such that $f(z_0)$ is a positive real number
101778
Show that there is $\eta\in(0,1)$ with $f''(\eta)=f(\eta)$
6636
Is there a positive function $f$ on real line such that $f(x)f(y)\le|x-y|, \forall x\in \mathbb Q , \forall y \in \mathbb R \setminus \mathbb Q$?
8854
Prove $f $ is identically zero if $f(0)=0$ and $|f'(x)|\le|f(x)|$
144589
Proving that if $f(x) \le g(x)$ then $f(x_0) \le g(x_0)$
113343
$f$ is constant if derivative equals zero
69695
$f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $[a,b]$
72856
Show $f$ is constant if $|f(x)-f(y)|\leq (x-y)^2$.
103706
If $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then there is a $c$ with $f(c) + f''(c) = 0$
108060
Suppose $f:[0,\infty]\rightarrow$ to R and has continuous $f'(x)$ and $f''(x)$ f(x) → 0 as x → ∞. Show that f′(x)→0 as x→∞