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Global and local Lipschitz proof

  • Thread starter Liferider
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  • #1
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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]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?
 

Answers and Replies

  • #2
43
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Ok, f(x) and f'(x) are continuous throughout R+. This can be proven by limits. So therefore f(x) is by definition locally Lipschitz in x on R+.
 

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