$f$ has a local maximum value at every point in $(a,b)$. Show that $f$ is constant.
108997
Continuous functions that attain local extrema at every point
69804
Prove that if $f$ is entire and $\vert f(z^2) \vert \leq 2 \vert f(z) \vert$, then $f$ is constant
20192
Prove that: $(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$ where $(a,b) \in \mathbb{R}^2$
35787
An entire function with a bound on its integral is constant
3885
Maximum and minimum of of $f(x)=|x-1|+|x-2|+|x-3|$
776
Entire function with positive real part is constant (no Picard)
82001
How to prove the function is a constant
84103
Let $f(z)$ be entire function. Show that if $f(z)$ is real when $|z| = 1$, then $f(z)$ must be a constant function using Maximum Modulus theorem
80421
Show that $a - b \mid f(a) - f(b)$
22294
Maximum and minimum value of $\int_0^1 f(x)dx $ given $|f'(x)|<2$
33308
Unique local extremum is absolute extremum for continuous functions
72856
Show $f$ is constant if $|f(x)-f(y)|\leq (x-y)^2$.
105768
Proof involving absolute value and maximums
11158
Proof that a continuous function with $f(x) = f(x^2)$ is constant.
39921
show that f is constant on I
113343
$f$ is constant if derivative equals zero
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