Chapter 14.7, Problem 5E

To determine

(a) Show that the critical points satisfy the equations $y\left(y-2x+1\right)=0,x\left(2y-x+1\right)=0$

(b) Show that the function has three critical points where $x=0$ or $y=0$(or both) and one critical point where $x,y$ are non-zero

(c) The nature of the critical points using the second derivative test.