Let $f:[0,1]\to\Bbb{R}$ a continuous function which is differentiable in $(0,1)$, but is not in $0$ and $1$ I need to draw a graphic which the function is differentiable in whole $(0,1)$ but is not in $0$ and $1$.
I just can imagine the function $f(x)=cotg(\frac{x}{\pi})$ but this $f$ is not well-defined in $[0,1]$, despiste being not differentiable at $0$ and $1$.

Hint: First, find a continuous function $g$ on $[0,1]$ differentiable everywhere except $0$. Let $h(x)=g(x)\cdot(x-\frac{1}{2})^2$ -- it will have the same properties, but the derivative at $\frac{1}{2}$ will be $0$. Then put $$f(x)=\begin{cases} h(x) \textrm{ if }x<\frac{1}{2}\\ h(1-x)\textrm{ if }x\geq \frac{1}{2}.\end{cases}$$
