f: R → R and $|f'(x)| ≤ |f(x)|$
33247
Does $f(0)=0$ and $\left|f^\prime(x)\right|\leq\left|f(x)\right|$ imply $f(x)=0$?
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
138544
For which values of $x$, will $f (x) . f '(x) < 0$?
89429
Prove $\sup \left| f'\left( x\right) \right| ^{2}\leqslant 4\sup \left| f\left( x\right) \right| \sup \left| f''\left( x\right) \right| $
13270
Prove $\exists \xi \in (a,b):f'(\xi)<1+f^2(\xi)$
31685
Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$
69378
The derivative of $x!$ and its continuity
58943
If $f'(x)\le g'(x)$, prove $f(x)\le g(x)$
85535
Finding maximum of $|f'(i)|$
74100
How do you solve $f'(x) = f(f(x))$?
85739
Show that $f(x) = 0$ for all $x \in [a,b]$ given $|f'(x)| \leq C|f(x)| $
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
63526
Proving that $(\sup_{x\in R}|f'(x)|)^2\leq 4\sup_{x\in R}|f(x)|\cdot\sup_{x\in R}|f''(x)|$.
77493
Classic $c_r$-inequality in $l_r$ space: $E(|X+Y|^r)\leq c_r[E(|X|^r)+E(|Y|^r)]$
35889
Suppose that f(0) = f(1) = 0 and x ∈ (0, 1). Prove that there exists c ∈ (0, 1) such that f'(c) = f(x).
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
56958
bounding a $C^1$ function that upholds $f'(t)\leq 1-f(t)^2$