IMO $2011$ problem $3$, how can I prove that $f(x) = 0, \; \forall \; x \leq 0 $?
69707
If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, then prove that $f(x) = 0$ for all $x ≤ 0$.
105316
Prove : $|x - y| \leqslant \epsilon$ $\forall \epsilon > 0$ iff $x = y$
57026
$f(0)=f'(0)=f'(1)=0$ and $f(1)=1$ implies $\max|f''|\geq 4$
145573
How to show that $f$ is a zero function?
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
84313
$|f(z)|\le 1-|z|\forall z\in D$, we need to show $f\equiv 0$
72660
How can I show that $f$ must be zero if $\int fg$ is always zero?
2414
If $f \in \operatorname{Hol}(D)$, $f(\frac{1}{2}) + f(-\frac{1}{2}) = 0$, prove that $|f(0)| \leq \frac{1}{4}$
74583
Prove that $f'(0)=L$.
6825
If $f: \mathbb Q\to \mathbb Q$ is a homomorphism, prove that $f(x)=0$ for all $x\in\mathbb Q$ or $f(x)=x$ for all $x$ in $\mathbb Q$.
87567
How to prove $1+x \leq e^x~\forall x \in \mathbb{R}?$
25467
Prove that $\lim f(x) =0$ and $\lim (f(2x)-f(x))/x =0$ imply $\lim f(x)/x =0$
151958
How to show $f'(0)$ exist and is equal to $1$?
132093
Solve $f(f(x))=f(x)$
33247
Does $f(0)=0$ and $\left|f^\prime(x)\right|\leq\left|f(x)\right|$ imply $f(x)=0$?
105700
Proving $\,f$ is constant.
33989
If $\int_0^1 f(x)x^n \ dx=0$ for every $n$, then $f=0$.