Question 1
Find and classify the critical points of the Lagrange function L(x
1, x
2,..., x
10, λ) corresponding to the problem:
extremize

subject to

x
i =

.
Question 2
Starfleet Command has given Captain Kirk a subspace amplifier to channel communications among n star systems having galactic Cartesian coordinates (x
k, y
k, z
k) for k = 1, 2,..., n. To what point in space should Captain Kirk take the Enterprise to place the amplifier so as to minimize the sum of the squares of its distances from the n star systems?
◦ the point

◦ the point

◦ the point

◦ the point

◦ the point