I want to find out if a function is lipschitz continuous.

Take for example the function on

I know it's not lipschitz continuous since the graph's slope goes to +/-infinity when x approaches 0, but is this argument sufficient?

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- Dec 14th 2011, 12:53 AMmadflame991[SOLVED] Lipschitz continuity
I want to find out if a function is lipschitz continuous.

Take for example the function on

I know it's not lipschitz continuous since the graph's slope goes to +/-infinity when x approaches 0, but is this argument sufficient? - Dec 14th 2011, 05:46 AMemakarovRe: Lipschitz continuity
According to this theorem, yes. We have that is a Banach space and is a convex open subset of . Also, is continuous on the closure of A and differentiable on A. Therefore, is Lipschitz continuous on iff is bounded on A, which it is not.

However, it is easiest to show that is not Lipschitz continuous on [0,1) by definition since is not bounded on that interval.