Suppose f is not one-one on the interval then there exists u, v in (a,b) such that f(u)=f(v).Use the Mean Value Theorem to show that:

a)Suppose f is a diferentiable function on the interval a < b, and suppose f '(x) is not equal to 0 for all x Element Symbol (a,b). Show that f is one-to-one on the interval (a,b).

Then by the mean value theorem there exists a point w in (u,v) such that f'(w)=0, a contradiction.

RonL