Determine number of minima with Hessian matrix

[mawith]

I have a function \(\displaystyle f:R^5->R\) which is quadratic and in every local minimum the Hessian matrix is positive definite.
Hessian matrix is square, have second partial derivatives and positive definite means, there is really minimum not maximum or saddle point. What is the greatest and smallest possible number of local minimums of the function?

 

[Steven G]

Please read the guideline for this site which basically says that if you show no work then you get no help. If you do not show any work then we do not know where you are stuck, what method you are trying to use, etc etc.

Please show some attempt at working this problem and you will be given leading hints so that you arrive at the solution.

 

[mawith]

For example if I have this function from \(\displaystyle R^5->R: f(x,y,z,a,b)=x^2*y^0*z^0*a^0*b^0\) then smalles possible number of minimum is one? If I have \(\displaystyle f(x,y,z,a,b)=x^2*y^2*z^2*a^2*b^2\) then the greatest number of possible minimum is 5? I have no other ideas