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Nov 29, 2017 at 15:16 comment added Bazin Thanks for the 1 D argument. You write that the same argument works in $n$ dimensions, which is not absolutely clear to me since the representation of $f$ via $\nabla f$ cannot obviously be used in the same way.
Nov 29, 2017 at 14:55 history answered Alexandre Eremenko CC BY-SA 3.0