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**The attempt at a solution**

using Lagrange multipliers, we solve the equations [tex]\nabla[/tex]f=[tex]\lambda[/tex][tex]\nabla[/tex]g ,which can be written as

[tex]f_{x}[/tex]=[tex]\lambda[/tex][tex]g_{x}[/tex]

[tex]f_{y}[/tex]=[tex]\lambda[/tex][tex]g_{y}[/tex]

g(x,y)=36

or as

y=[tex]\lambda[/tex]8x

x=[tex]\lambda[/tex]18y

[tex]4x^2{}[/tex]+[tex]9y^2{}[/tex]=36

it's pretty much all done but can somebody solve this? cause i have some doubts about which are the extreme points