Obvious but unprovable: If $f'$ is the zero function on $\mathbb Q$, then $f$ is constant
87743
Is a function whose derivative vanishes at rationals constant?
62640
Show a given analytic function is constant
56978
How to Prove that if $f(z)$ is entire, and $f(z+i) = f(z), f(z+1) = f(z)$, then $f(z)$ is constant?
145573
How to show that $f$ is a zero function?
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?
132478
Prove that continuous functions mapping irrationals to rationals must be constant
74810
A function $f$ such that $f' = 0$ when $x < 0$ and $f' = 1$ when $x \geq 0$?
106290
Prove a function is constant. (complex analysis)
158647
If $|f(z)|\le |f(z^2)|$ then prove that $f$ is constant
110395
Integrable function $f$ on $\mathbb R$ does not imply that limit $f(x)$ is zero
69695
$f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $[a,b]$
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
103706
If $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then there is a $c$ with $f(c) + f''(c) = 0$
145919
If $f: \Bbb{R}\rightarrow\Bbb{R}$ is continuous at $0$ and $f(x)=f(2x)$ for each $x\in\Bbb{R}$ then $f$ is constant.
96539
is $f$ constant or dilation
89050
If $|f(z)|\leq |f(z^2)|$ on the unit disk, show that $f$ is a constant function.
13150
If the derivative of $f$ is never zero, then $f$ is one-to-one