Solving for critical points and classification using Maple

Question

I am trying to help a friend on an assignment using Maple. The question gives a function $$f(x,y,z)= x+\frac{y^2}{4(x-5)}+\frac{z^2}{y-3}+\frac{2}{z+5}$$ and asks to find and classify the critical points of the function.

The assignment requires the use of these commands:

 diff, solve, Hessian, assign, SubMatrix, Determinant

Letting f be the original function, what I have so far is:

 A:=diff(f,x)
 B:=diff(f,y)
 C:=diff(f,z)
 solve(A=0,x)
 solve(B=0,y)
 solve(C=0,z)

However, I do not know how to proceed from here. Any help would be greatly appreciated!