Prove $f(x)\equiv 0$
131000
A proof of a criterion of vanishing of a function.
82001
How to prove the function is a constant
75653
Prove that $|f ''|\ge 4$
131876
Show that $\int_{a}^{b}{x^{n}f(x)dx}=0$, then $f=0$
64955
Show that there are $ a,b \geq 0 $ so that $ |f(x)| \leq ax+b, \forall x \geq 0.$
71225
$f(0)=0$ and $\lim_{x \to \infty}f(x)=0$. Show there's $x_0$ such that $f'(x_0)=0$
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 $x ≤ 0$.
116056
Prove that $|f(x)-f(y)|\le|x-y|$ for all $x$ and $y$.
84313
$|f(z)|\le 1-|z|\forall z\in D$, we need to show $f\equiv 0$
8913
Show that there is $\xi$ s.t. $f(\xi)=f\left(\xi+\frac{1}{n}\right)$
135577
Prove the existence of $c$ such that $f'(c) = 2c(f(c) - f(0))$
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
145573
How to show that $f$ is a zero function?
56127
Prove a function is constant under certain conditions
149287
Prove that $A,B>0$ and $A_{ij}0$
67292
Prove that $\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$
82567
Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $