Uniform Boundedness of Derivative Sequence of C^1([a,b],R) Functions

[johnson12]

Im having trouble showing that given a sequence of uniformly bounded C^1([a,b],R) functions,
the derivative sequence is uniformly bounded.
Any suggestions are helpfull

 

[Dick]

If by 'uniformly bounded', you mean |f_n(x)|<M for some constant M, it's not true that the derivatives are necessarily bounded.

 

[johnson12]

Youre right, the reason I ask is b/c I am trying to prove that every bounded sequence in C^1 has a convergent subsequence, Arzela Ascoli type problem.

 

[Dick]

What do you mean by a 'bounded sequence' in C^1? sin(n*x) is a bounded sequence in C^1 (in the sense |f_n|<=1). But it has no convergent subsequence. You need some sort of premise to get the equicontinuity from.