Minimize 
subject to 
. The Lagrangian would be
and has partial derivatives
Setting each partial derivative to 0, we have
From the third equation, it follows that either
or 
. In the second case, we arrive at a contradiction:
since both
and 
must be non-negative, yet this would mean e.g. 
. So it must be that .
The first and second equations then tell us that
from which we obtain
.
Thus the points on the cone closest to (16, 6, 0) are
.
and has partial derivatives
Setting each partial derivative to 0, we have
From the third equation, it follows that either
since both
The first and second equations then tell us that
from which we obtain
Thus the points on the cone closest to (16, 6, 0) are