Question

Need help with Lagrange multipliers, please

Answer 1

i understand, the equation they got, of gradient f=lambda(gradient g)

but how did they find y=0 and lambad= plus or minus 2

Answer 2

i am so lost

Answer 3

they start with
y i + xj -(L/4) x i - L y j=0 (I think they have a typo, a + where it should be -)
this is the same as
(1) y= (L/4) x (equate the i components)
(2) x= Ly (the j components)

use the definition of x given by (2) in equation (1)
(3) y= (L/4)(Ly)
y= (L^2/4) y
y-(L^2/4)y = 0
y(1- L^2/4)= 0

y=0 or (1-L^2/4)=0
L^2= 4, L=±2

Answer 4

Here is the lagrange multiplier problem using partial differentiation.

Answer 5

Thanks, i see whats going on now