Say G is a part (wich is open) of R^n, f and g are functions from G to R (f:G->R, g:G->R) and both are differentiable (and the differential is continues). If f(p)=0, Df(p)#0 and g has an extremum on p (f^-1(0)) then there is a delta (element of R) for wich you can write: Dg(p)=delta*Df(p)

But if g has an extremum on p then wouldn't Dg(p) = 0?

thx in advance