This extreme value problem has a solution with both a maximum value and a minimum value. use lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x1, x2, xn) = x1 + x2 + + xn; x12 + x22 + + xn2 = 4

The Lagrangian is

with partial derivatives (all set equal to 0)

for , and

Substituting each into the second sum gives

Then we get two critical points,

or

At these points we get a value of , i.e. a maximum value of and a minimum value of .

i think the answer is d im not sure