Periodic function such that $f(x)+f'(x)\geq 0$ is non-negative.
141522
$f$ is T periodic and $f(x) + f'(x) \ge 0 \Rightarrow f(x) \ge 0$
135577
Prove the existence of $c$ such that $f'(c) = 2c(f(c) - f(0))$
56958
bounding a $C^1$ function that upholds $f'(t)\leq 1-f(t)^2$
54297
Is $f(x)=10$ a periodic function?
18082
A continuous function that attains neither its minimum nor its maximum at any open interval is monotone
90892
Is a function increasing if the derivative is positive except at one point of an interval?
120676
A certain element which makes functionals positive
28315
Monotone functions and non-vanishing of derivative
152701
A question on periodicity of complex functions
31308
Does there exist some strictly positive function such that both the derivative and second derivative are strictly negative?
99782
$a_{n+1}=|a_n|-a_{n-1} \implies a_n \; \text{is periodic}$
103285
Limit of a periodic function
26388
proof that function is constant
158230
prove that a non constant periodic, continuous function has a "smallest period"
109091
Why do non-constant periodic functions have no limit at infinity?
156778
Finding functions satisfying $f(f(x))+f(x)+x=0$
96495
Periodicity of a Function Given the Functional Equation $f(x+a)=\frac12+\sqrt{f(x)-\big(f(x)\big)^2}$