• Support PF! Buy your school textbooks, materials and every day products Here!

Lipschitz continuity

  • #1

Homework Statement



Show f(x) = x^(1/3) is not lipschitz continuous on (-1,1).

Homework Equations



I have abs(f(x)-f(y)) <= k*abs(x-y)

when I try to show that there is no K to satisfy I have problems
 

Answers and Replies

  • #2
1,101
3
Examine |f'(x)| as x tends to 0.
 

Related Threads on Lipschitz continuity

  • Last Post
Replies
1
Views
374
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
1
Views
796
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
Replies
5
Views
1K
Replies
1
Views
1K
Replies
5
Views
1K
  • Last Post
Replies
2
Views
3K
Top