## If $f’=[f]^2$ and $f(0)=0$, what we can say about $f$?

Let $$f:\mathbb{R}\to\mathbb{R}$$ be differentiable and $$f(0)=0$$ s.t. $$\forall x \in \mathbb{R}$$ we have

$$f'(x)=[f(x)]^2,$$

where $$[x]$$ is the least integer greater than or equal to $$x.$$

Show that $$f(x)=0$$, for every $$x\in \mathbb{R}$$.

I tried to take the Riemann integral of both sides and I got stuck. I appreciate any help.