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
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
If yes give an example, and if not, show why
Please help
The answer to (1) is probably most easily obtained using the mean value theorem, which is a generalization of Rolle's theorem.
As noted in the comments, there are plenty of suitable examples for (2). In particular, a straight line passing through those two points will do.