1. The problem statement, all variables and given/known data f(x,y)= 16(y^2) +(x^4) y + 4(x^2) + 4 My problem is recognizing which critical points to consider valuables. 2. Relevant equations fxx, fyy, fxy, and second partials test. D=fxx(fyy)- (fxy)^2 3. The attempt at a solution I found: fx=0 4(x^3)y +8x=0 (x^2) y= -2 Now, from here I can discern that either x=+-1 , y= -2 **this solution is not considered in the solutions manual. Anyone care to explain** OR x=2, y= -(1/2) OR x= -2, y= -1/2 Also, I was thinking about plugging in values of the other fy=0 part. It gets even more complicated. Now: fy=0 32y + (x^4) =0 y= -(x^4)/32 From here the only thing I thought about was x=0, y=0. I also thought about solving for y and replacing on the other fx equation, but things don't look good and the solutions shows that it's wrong. Can anyone give me tips to discern critical points? Thank you.