
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 xx[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].