Prove that there is no differentiable function f(x) defined on (−∞,∞) such that f′(0)=1, but f′(x)≥2 for x≠0.
So I use contradiction method, suppose there exists a function f(x) with those properties, using the definition of limit gives me
f′(0)=limh→0∣f(0+h)−f(0)h∣=1 and f′(x0)=limh→0∣f(x0+h)−f(x0)h∣ ≥2 for x0∈R but x0≠0. I don't know how to come up with a contradiction. Please help.
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