Level Sets and Degenerate Critical Points

1. Mar 28, 2012

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.

2. Mar 29, 2012

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.

3. Mar 29, 2012

autarch

Now you know how I feel.