For Lipschitz condition:

for constant k on [a,b] if there is a constant k such that for all x,y in [a,b]

|Tx -Ty| less than or equal to k|x-y|

I have to show if:

f(t,x)=|x|^(1/2)

satisfies the condition

I think it would but i am having trouble proving this. Is there a way to find a minimum value k such that all Tx-Ty satisfy this condition?