Question

If f'(x)>=0 for x>=0 and f(x) tends to a finite limit. Does f'(x) tend to 0?

Answer 1

Think about the definition of the derivative. Conventionally, it's defined as a limit. What will happen to that limit if f(x) tends to a finite limit?

Answer 2

I think it tends to 0, but I think it's dangerous to just assume that, especially since I know the same thing without the x>=0 is definitely not true.