Let $\displaystyle f0,1) \rightarrow \mathbb {R} $ be differentiable and let $\displaystyle f'(x)$ be Bounded. Show that $\displaystyle \lim _{x \rightarrow 0^+ } f(x) $ exist.

Idea so far.

So if I define a sequence that converges to a point at 0, f would be able to able to map that into the co-domain, would that be the right start?

Thanks.