Thread: 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

Originally Posted by ajskim

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...

Tonio

I was hoping to find a non-trivial example, but thank you. Yeah, I agree that Sard's probably isn't applicable here.

Oops! I meant critical values, not critical points

Solved! Sum of bump functions