R->R function in C∞ whose set of critical points are dense
I need to find such a function. Any ideas about how to approach this? We have just covered Sard's theorem if that provides some sort of insight on how I should tackle this.
Thanks
I need to find such a function. Any ideas about how to approach this? We have just covered Sard's theorem if that provides some sort of insight on how I should tackle this.
Thanks
Sard's theorem is trivial for one variable functions, as the set of critical points of ,
so I don't think it'll help a lot here.
Of course, constant is a trivial example, but I'm not sure how to construct other examples, or even whether there exist...