How would one show that if there is a number c for which g'(c)=0, then every point on the level set {(x,y)|H(x,y)=c} is a degenerate critical point of f?(adsbygoogle = window.adsbygoogle || []).push({});

I know that the question may seem vague, but this is the question as it was given to me by my professor. It is something to think about, but. I would appreciate a comprehensive answer; however, any comments would also be appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Level Sets and Degenerate Critical Points

**Physics Forums | Science Articles, Homework Help, Discussion**