Lagrange multiplier (i'm i doing this right?)?

[sampe...@yahoo.com]

Hi guy's, could some please tell me if im doing this right!?

the question that was asked:

f (x, y) = 18y + 6x − 2xy
Calculate (by Lagrange multiplier) the stationairie points of f(x,y),
under the constraint:

x − y2 = 0

Also calculate the value of the function in the stationairie pionts
and also calculate 'Lagrange multiplier' (λ) for the(se) pionts.

So what i did:

L(x,y,λ)= 18y+6x-2xy-λ(x-y^2)

L'x = 6-2y-λ=0
L'y = 18-2x-2λy=0

constraint: x-y^2=0
This means: x=y^2
y= √x or y=-√x

18-2x-2λy = 0

18-2y^2-2λy=0

λ=(18-2y^2)/2y = (6-2y)/1

18-2y^2 = 12y-4y^2

18= 12y-2y^2

This gives me:
-2y^2+12y-18=0

On this is used the ABC formula witch gave me: X(1)= 3 and X(2)= 3.
Meaning x = 3
So y=√3 or y=-√3

Corresponding points (3,√3) (3,-√3)


I would really really appreciate it if someone could check this for
me!!
Thank you for your attention :-)
p.s. sorry if its a bit me messy