Math Help - Lagrange Multipliers

1. Lagrange Multipliers

'Find the coordinates of the point on the sphere (x − 2)^2 + y^2 + z^2 = 1 which is at the greatest distance from the point (1,2,3). Show that this distance is 1 +Sqrt(14).'

The problem here is that i am getting 2 different lagrange multipliers. Namely
1+Sqrt(15) and 1-Sqrt(15). How do i know which one is the right one to use?

Thanks

2. Originally Posted by DeFacto
'Find the coordinates of the point on the sphere (x − 2)^2 + y^2 + z^2 = 1 which is at the greatest distance from the point (1,2,3). Show that this distance is 1 +Sqrt(14).'

The problem here is that i am getting 2 different lagrange multipliers. Namely
1+Sqrt(15) and 1-Sqrt(15). How do i know which one is the right one to use?

Thanks
One will correspond to the maximum and the other the minimum distance.

CB