- #1
aicort
- 6
- 0
determine, if any, the maximum and minimum values of the scalar field f (x, y) = xy subject to the constraint [tex]4x^2{}[/tex]+[tex]9y^2{}[/tex]=36
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
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