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.

Please someone help me with this Mean Value Theorem Proof. Thanks