Let $f:\mathbb{R}\to(0,\infty)$ be a differentiable function. For all $x\in\mathbb{R}$ $f'(x)=f(f(x)).$ Then show that such function does not exists
124894
Looking for a function such that...
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→∞
143874
Limit of derivative is zero. Does it imply a limit for f(x)?
136980
Prove there exists $a\in \Bbb{R}$ such that $f'(a)=0$.
2717
Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
13202
Prove that there exists at least one $x_0\in\mathbb{R}$, such that $f(x_0)+f''(x_0)=0$
110395
Integrable function $f$ on $\mathbb R$ does not imply that limit $f(x)$ is zero
153510
Questions about the existence of a function
3922
How to prove that there exist no functions $f,g:\Bbb{R}\to\Bbb{R}$ such that $f(g(x))=x^{2018}$ and $g(f(x))=x^{2019}$?
41173
If $f\in S_\infty$ and $\int_{\mathbb{R}}x^pf(x)d\mu=0$ for all $p\in\mathbb{N}$ then $f\equiv 0$?
94944
Differentiable functions satisfying $f'(f(x))=f(f'(x))$
28949
Prove $f(x) = 0 $for all $x \in [0, \infty)$ when $|f'(x)| \leq |f(x)|$
70458
Show that it is possible that the limit $\displaystyle{\lim_{x \rightarrow +\infty} f'(x)} $ does not exist.
158940
Give an example of a continuous function $f : [0, ∞) \mapsto [0, ∞)$ such that $\int_{0}^{\infty}f(x)dx$ exists but $f$ is unbounded.
44129
If $f:\mathbb{R}\rightarrow \mathbb{R}$ is differentiable and $\lim_{x\to \infty } f^\prime(x)=0$ show that $\lim _{x\to \infty } (f(x+1)-f(x))=0$.
17154
Does a non-trivial solution exist for $f'(x)=f(f(x))$?
44761
Is $f'(x)-3f(x) = 0$ subspace of differentiable functions $f\colon (0,1)\to \mathbb{R}$