I am having a problem with this exercise. Please help.
Is it possible to find a function $f$ with a continuous derivative $f'$, such that $f'(x)>0$ and
- $f(0)=1,\;f(1)=0$,
- $f(0)=-1,\;f(1)=0$?
If yes give an example, and if not, show why
Please help