$$f:(0,1)\rightarrow [0,1]$$ is a differentiable function . Is it uniformly continuous then $?$
Now $f$ being differentiable on $(0,1)$ is continuous , that is easy. Now I could say it is uniformly continuous if the differentiability on $(0,1)$ implied continuity on $[0,1]$. What the range being the closure of the domain contributes here $?$
Please give some lead on how to proceed .
Thanks for any help.