A function f(x)f(x)f(x) is continuous on R\mathbb{R}R and satisfies ∣f(x)−f(y)∣≤∣x−y∣|f(x) - f(y)| \le \sqrt{|x-y|}∣f(x)−f(y)∣≤∣x−y∣. What can be said about fff?
fff must be differentiable
fff is Hölder continuous
fff is Lipschitz continuous
fff must be constant