1. The problem statement, all variables and given/known data (I don't have my book with me, so this may not be the correct word-for-word representation of the exercise) Suppose f(x) is differentiable on the whole real line. Show that f(x) is constant if for all real numbers x and y, |f(x)-f(y)| ≤ (x-y)2. 2. Relevant equations Definition of a derivative 3. The attempt at a solution f(x)-f(y) ≤ |f(x)-f(y)|, so by basic algebra we have [f(x)-f(y)]/(x-y) ≤ x - y. Letting x approach y on both sides of the inequality yields f '(x) ≤ 0. ........ Now I somehow need to show that f '(x) ≥ 0. Ideas?