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Apr 15 at 20:28 vote accept Heinrich A
Apr 15 at 19:36 comment added Iosif Pinelis @HeinrichA : I don't think so. I think you can modify this example to have $(p-1)^4$ in place of $(p-1)^2$ and then use something like $f(x)=c+x^2$.
Apr 15 at 19:33 history edited Iosif Pinelis CC BY-SA 4.0
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Apr 15 at 19:33 comment added Heinrich A Thanks. Does it help if all functions are smooth?
Apr 15 at 19:24 history answered Iosif Pinelis CC BY-SA 4.0