Just to start you in the right direction, take as in the hint, and define Now apply the mean value theorem to the function in the interval from 0 to x. Remembering that and that , you should be able to conclude that for some t between 0 and x. But . So if has been chosen so that , it will follow that (for all ), as required.

Now you have to repeat a similar argument, by integrating and using the mean value theorem again, to get the corresponding result at the level of f.