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## Homework Statement

f(x)={0 for x<0, [itex]\sqrt{x}[/itex] else}

a) Is f(x) globally Lipschitz? Explain

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

## Homework Equations

## The Attempt at a Solution

a) f(x) is not globally Lipschitz in x on [a,b]xR

^{n}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?