Lipschitz Continuity Proof: f(x) = x^(1/3) on (-1,1) Has No Lipschitz Constant

[CarmineCortez]

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

 

[snipez90]

Examine |f'(x)| as x tends to 0.