Hello, a1007!
We have: .
Subtract the equations: .
Factor: .
We have two cases to consider: .
Substitute [1] into
. . Hence: .
Substitute [2] into
. . Hence: .
hey i have this problem where
z = xy(6-x-y) when multiplying out and differentiating with respect to x i get:
dz/dx = 6y - 2xy -y^2 and y dz/dy = 6x - x^2 - 2xy
I understand with the -2xy you can make the equations equal and find stationary points, which i got as (0,0) (6,0) and (0,6) but once checking the answers there was a further point (2,2) and I don't understand on how to obtain this stationary point, help would be much appreciated than you