Give an example of a function f:U⟶R
uniformly differentiable with unbounded derivative f′, U⊂R open set.
Any hints would be appreciated.
Answer
Take f(x)=x3/2 on U=[0,∞). Then f′(x)=(3/2)x1/2, which is uniformly continuous on U. By the MVT, f′ is uniformly differentiable on [0,∞). Since f′ is unbounded, we have an example.
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