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

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- September 29th 2010, 04:23 PMajskimR->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 - September 29th 2010, 05:14 PMtonio
- September 29th 2010, 06:17 PMajskim
I was hoping to find a non-trivial example, but thank you. Yeah, I agree that Sard's probably isn't applicable here.

- September 29th 2010, 06:39 PMajskim
Oops! I meant critical values, not critical points

- September 29th 2010, 08:44 PMajskim
Solved! Sum of bump functions