1. The problem statement, all variables and given/known data 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). b) Assume that |f ' (x)| < or equal to C < 1 for all x. Show that f (x) = x has at most one solution. 2. Relevant equations 3. The attempt at a solution Suppose f is not one-one on the interval then there exists u, v in (a,b) such that f(u)=f(v). Then by the mean value theorem there exists a point w in (u,v) such that f'(w)=0, a contradiction. Don't know where to go after that.