Sunday, 28 July 2019

Analysis Problem on Differentiability

Prove that there is no differentiable function f(x) defined on (,) such that f(0)=1, but f(x)2 for x0.



So I use contradiction method, suppose there exists a function f(x) with those properties, using the definition of limit gives me



f(0)=limh0f(0+h)f(0)h=1 and f(x0)=limh0f(x0+h)f(x0)h 2 for x0R but x00. I don't know how to come up with a contradiction. Please help.

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