holder condition

Let f: [a,b] -> R be a real function

It is said that f satisfies the Holder condtion of order alpha >0 if there exists an M>0 and some tilda>0 such that for all x[0] in [a,b] and all x in [a,b] with 0<| x - x[0] | < tilda it holds |f(x) - f(x[0]\ < M |x-x[0]|^alpha

iv already shown that f:[a,b] -> R satisfies the Holder condition of order aplha >0 at any x[0] in [a,b] whcih makes f continious

but now im stuck on the part where i want to show that f:[a,b] -> R satisfies the Holder condition of ORDER aplha >1 at any x[0] in [a,b]. then f is differentiable at any x[0] in [a,b].