Thread: differentiability

Given f: (a,b) -> R is differentiable at p in (a,b)
1. prove f'(p) = lim n->infinity (n[f(p+1/n)-f(p)])
I already this this part using the definition of f'(p)

2. By example, show that the existence of the limit of the sequence {[f(p+1/n)-f(p)]} doesn't imply the existence of f'(p)

I don't know how to go about this one. Please provide some hints

Originally Posted by inthequestofproofs

Given f: (a,b) -> R is differentiable at p in (a,b)
1. prove f'(p) = lim n->infinity (n[f(p+1/n)-f(p)])
I already this this part using the definition of f'(p)

2. By example, show that the existence of the limit of the sequence {[f(p+1/n)-f(p)]} doesn't imply the existence of f'(p)

I don't know how to go about this one. Please provide some hints

Surely, you have already seen examples of functions that are not differentiable. For example, is not differentiable at x=0. Or, to shift the whole thing from 0 to p, you can take .