Prove that $f'(x)<kf(x)$. What can the biggest value of k
104263
How to show that $f'(x)<2f(x)$
88580
Finding the maximum value of $\int_0^1 f^3(x)dx$
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
54321
Questions about $f: \mathbb{R} \rightarrow \mathbb{R}$ with bounded derivative
3772
About the continuity of the function $f(x) = \sum\limits_k2^{-k}\mathbf 1_{q_k \leq x}$
59063
$f(f(x))=f(x)$ question
54729
Prove that $f$ has a fixed point .
136980
Prove there exists $a\in \Bbb{R}$ such that $f'(a)=0$.
21954
A question about $f(x)\equiv 0$
32506
Prove $kf(x)+f'(x)=0 $ when conditions of Rolle's theorem are satisfied .
52711
Prove that the sequence $\{v_n\}$ converges to the maximum value of $f$ on $[a,b]$
111186
Proving that if $|f''(x)| \le A$ then $|f'(x)| \le A/2$
40905
Prove $f(\sum^k_{i=1} \alpha_i x_i) \leq \sum^k_{i=1} \alpha_i f(x_i) $ for a convex function f
79281
Let $f : X \to Y$ be a function and $E \subseteq X$ and $F \subseteq X$. Show that in general
20192
Prove that: $(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$ where $(a,b) \in \mathbb{R}^2$
24683
For i.i.d. $\{X_n\}$ proving $\frac1n\max\limits_{1\leqslant k\leqslant n}|X_k|\xrightarrow{\mathrm{a.s.}}0\Leftrightarrow E(|X_1|)<+∞$
17154
Does a non-trivial solution exist for $f'(x)=f(f(x))$?