If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
112923
Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}$
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
44336
Is $\lim\limits_{x\to x_0}f'(x)=f'(x_0)$?
76580
If $f(\frac{1}{n})=0$ all $ n\to \mathbb{Z^{+}}$ then find $ f'(0)$?
61190
If all derivatives of $f$ are uniformly bounded by a common constant and $f(1/n) = 0$ for all $n$, is $f$ identically zero?
121771
Proof $f(x)\equiv 0$
23615
Why does zero derivative imply a function is locally constant?
71225
$f(0)=0$ and $\lim_{x \to \infty}f(x)=0$. Show there's $x_0$ such that $f'(x_0)=0$
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
77267
Given $f$ is continuous and $f(x)=f(e^{t}x)$ for all $x\in\mathbb{R}$ and $t\ge0$, show that $f$ is constant function
58901
Why is every such function constant: $f(x)=f(x^2)$ for $x \in [0,1]$?
32506
Prove $kf(x)+f'(x)=0 $ when conditions of Rolle's theorem are satisfied .
130322
Show that $f(x) = 0$ if $x = 0$ $f(x) = \text{exp}(-1/x^{2})$ if $x \neq 0$ is infinitely differentiable but not analytic at $x_{0} = 0$ `
41173
If $f\in S_\infty$ and $\int_{\mathbb{R}}x^pf(x)d\mu=0$ for all $p\in\mathbb{N}$ then $f\equiv 0$?
143874
Limit of derivative is zero. Does it imply a limit for f(x)?
85750
If $f(x)=\int_{x-1}^x f(s)ds$, is $f$ constant? Periodic?
74673
True or false: if $f'(c)<0$, then $f$ is concave down at $x=c$?