Chapter 9 - Multiveriable Calculus - 9.2 Partial Derivatives - 9.2 Exercises - Page 478: 36

$x=4 \rightarrow y=-18$ $x=0 \rightarrow x=0$

$f_{x}(x,y)=81x^{2} +72y =0$ $f_{y}(x,y)=72x +16y=0$ Solving the first equation for yields $y=\frac{-9x^{2}}{8}$ Substituting this into the second equation yields $72x +16(\frac{-9x^{2}}{8})=0$ $72x-18x^{2}=0$ $x=4 \rightarrow y=-18$ $x=0 \rightarrow x=0$