Chapter 9 - Multiveriable Calculus - 9.2 Partial Derivatives - 9.2 Exercises - Page 478: 33

x=-4 ; y=2

$f_{x}(x,y) = 12x +6y + 36=0$ $f_{y}(x,y)=12y +6x=0$ Solving the second equation for $x=\frac{-12y}{6}$ Substituting this into the first equation yields: $12(\frac{-12y}{6}) +6y +36=0$ $-24y+6y+36=0$ $y=2$ $\rightarrow x=-4$