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?
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?
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.