# Math Help - Lagrangian function.

1. ## Lagrangian function.

f(x,y)=2x^2+y^2 subject to the constraint of x+y=1.

I understand how to set it up and how to find f with respect to x y and L.

fx=4x+L
fy=2y+L
fL=x+y-1

So, again...I understand the cal part of it, but fail to remember the basic allgebra part. Please solve for x, y, and L (ie the critical point)

2. set $f_x, f_y$ and $f_L = 0$ then solve the system.

3. I know to set them equal to 0, but I'm not exactly sure how to solve from there. This may actually be the wrong section since this is just algebra...

4. $f_x=4x+L=0$ ...(1)
$f_y=2y+L=0$ ...(2)
$f_L=x+y-1=0$ ...(3)

Using (1) and (2)

$4x+L=2y+L$

Therefore

$4x=2y$

$2x=y$

Putting this into (3)

$x+2x-1=0$

$3x-1=0$

$x=\frac{1}{3}$

Can you solve it from here?

5. Oh, I feel dumb now... Thank you!