Let S be the set of all functions f: R → R satisfying |f(x) − f(y)|3 ≤ |x − y|5 for all x, y ∈ R. Then which of the following is/are true?
1
Every function in S is differentiable.
2
There exists a function f ∈ S such that f is differentiable, but f is not twice differentiable.
3
There exists a function f ∈ S such that f is twice differentiable, but f is not thrice differentiable.
4
Every function in S is infinitely differentiable.