- #1
Bacle
- 662
- 1
Hi, All:
Let f R-->R be differentiable. If |f'(x)|<M< oo, then f is uniformly continuous, e.g.,
by the MVTheorem. Is this conditions necessary too, i.e., if f:R-->R is differentiable
and uniformly continuous, does it follow that |f'(x)|<M<oo ?
Thanks.
Let f R-->R be differentiable. If |f'(x)|<M< oo, then f is uniformly continuous, e.g.,
by the MVTheorem. Is this conditions necessary too, i.e., if f:R-->R is differentiable
and uniformly continuous, does it follow that |f'(x)|<M<oo ?
Thanks.