Let
f : R--->R be differentiable with bounded derivative. Show that f is uniformly continuous.
(f(x) - f(y)) / (x - y) = f'(p)
for some p in (x,y) (by the mean value theorem) and if M > 0 is the bound
on all values of the derivative, so that
|f(x) - f(y) | / |x - y| <= M
or |f(x) - f(y)| <= M*|x-y| for all x,y.
Can you help please? Thanks