Let f : (a, b)--> R be differentiable on (a,b), and assume that f'(x) unequal 1 for all x in (a,b).
Show that there is at most one point c in (a,b) satsifying f(c) = c.
The Attempt at a Solution
I think that We need to use the mean value theorem for this problem.
This is what I know, but I'm not sure what I should use for my proof:
If we let c be n (a,b)
By definition f'(c)=lim: x-->c (f(x)-f(c)/x-c) assuming that f(x) is differentiable at c.
Also, the mean value theorem states that f[a,b]-->R is continuous on [a.b] and differentiable on (a,b), then there exists a point c in (a,b) so that f'(c)=f(b)-f(a)/b-a
Any help/hints would be great!