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.

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# Level Sets and Degenerate Critical Points

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