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)=lim=1 and f'(x_0) = \lim_{ h\to 0} \mid \frac {f(x_0+h)-f(x_0)}{h}\mid \geq 2 for x_0 \in R but x_0\neq 0. I don't know how to come up with a contradiction. Please help.

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