Let $F=\{f: \mathbb{R} \to\mathbb{R}:|f(x)-f(y)|\leq K|(x-y)^\alpha|\}$ for all $x,y\in\mathbb{R}$ and for some $\alpha >0$ and some $K > 0$ .
Which of the following is/are true?
1. Every $ f \in F$ is continuous
2. Every $f\in F$ is uniformly continuous
3. Every differentiable function $ f$ is in $F$
4. Every $f \in F$ is differentiable
The given condition is Lipchitz condition. So 1 and 2 are true. but what can I say about the others