f is constant?

From: Betelgeuse (betelgeuse_at_rigel.bellatrix)
Date: 02/27/05 

Date: Sun, 27 Feb 2005 23:54:53 GMT

Let f:(a,b)->R be differentiable in every point.
Assume also that I know that f'(x)=0 for
all x in A, where A is an open dense subset of (a,b).
Can I conclude that f is a constant function?
Thanks in advance.
Jenny