Level Sets and Degenerate Critical Points

[autarch]

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?


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.

 

[mathwonk]

it is not only vague but so vague as to be entirely meaningless. None of the relevant functions are defined or related to each other.

 

[autarch]

it is not only vague but so vague as to be entirely meaningless. None of the relevant functions are defined or related to each other.

Now you know how I feel.