Given the Generalized Rayleigh Quotient
Q(x) = (Ax dot x)/(Bx dot x)
and that A and B are both real n x n matrices, and B is positive definite.
How would I go about proving that Q(x) has at least one critical point. In class we restricted ||x|| to 1 so that ||x||^2 also is 1, but we never actually see ||x||^2 in this equation, so it doesn't seem like that would be helpful. If someone can please help me with where to start that'd be awesome! I know that taking the gradient is the first step, but after that I'm utterly confused.