Global and local Lipschitz proof

Liferider

Homework Statement

f(x)={0 for x<0, $\sqrt{x}$ else}

a) Is f(x) globally Lipschitz? Explain

b) Find the area for which f(x) is locally Lipschitz.

The Attempt at a Solution

a) f(x) is not globally Lipschitz in x on [a,b]xRn since there is a discontinuity at x=0.

b) I would think that f(x) is locally Lipschitz for all real positive numbers, R+, but how do I go about proving it?