Hi, I can't seem to get anywhere with the following problems:
1. Find a differentiable function f: R->R such that f'(0)=1 but f is not monotonically increasing on any interval (0,d).
2. Show that there exists a differentiable function f: R->R such that (f(x))^5 + f(x) + x = 0 for all x. [Hint: if f exists and has an inverse g what equations must g satisfy?]
Any help would be much appreciated.