4
I have discovered the following fact :
Let $f(x)$ be a $C^3$ function on $[0;\infty[$ and if we have the condition :
$$4|f'(x)|\geq f(x)^2$$ then
If $f(x)$ is negative on $[0;\infty[$ it implies that $f(x)$ is concave .
If $f(x)$ is positive on $[0;\infty[$ it implies that $f(x)$ is con...
