Max/Min using Lagrange Multipliers: F(x,y) = x^2 + y^2 ; xy = 1

[tnutty]

Homework Statement

Find max/min using L.M of the function :

F(x,y) = x^2 + y^2 ; xy = 1

let G(x,y) = xy - 1

F_x = 2x
F_y = 2y
G_x = y
G_y = x

F_x = L*G_x
F_y = L*G_y
G(x,y) = 1


1) 2x = L * y
2) 2y = L * x
3 ) xy = 1

Now I need to solve those equations.

so x = LY/2 ; y = LX/2

Then if I plug it in I get X = L^2/4 and similar for Y
Not sure how to approach that step

 

[Dick]

x=Ly/2 and y=Lx/2 doesn't tell you x=L^2/4. Try that again.