I'm given an n-dimensional function such that f(x1,x2,...,xn) = a1*x1 + a2*x2 +...+ an*xn where a1, a2, ...,an are all positive numbers. This is with the restraint that x1^2 + x2^2 + ... + xn^2 = 1 Using Lagrange multipliers (I'll use 'L' for Lambda): a1 = L(2*x1) a2 = L(2*x2) ... an = L(2*xn) Solving for L, L = a1/(2*x1) = a2/(2*x2) = ... = an(2*xn)  So, generally, xn = an/(2*L). Plugging into the constraint function, I get: (a1/2*L)^2 + (a2/2*L)^2 + ... + (an/2*L)^2 = 1 (1/4*l^2)*(a1^2 + a2^2 + ... + an^2) = 1 L = sqrt(a1^2 + a2^2 + ... + an^2)/2 So, for each x, generally, xn = an/sqrt(a1^2 + a2^2 + ... an^2)  Which implies that a1 = a2 = ... = an from  a1/(2*L) = a2/(2*L) = ... = an/(2*L) So  is basically my critical point. Plugging back into f(...) I get f(x1,x2,...,xn) = a1*(a1/sqrt(a1^2 + a2^2 + ... + an^2)) ...etc <=> ... (a1^2 + a2^2 + ... + an^2)/sqrt(a1^2 + a2^2 + ... + an^2) Furthermore.... <=> ... sqrt(a1^2 + a2^2 + ... + an^2) Since a1 = a2 = ... = an, then we can say (using an arbitrary (a)) <=> .... sqrt(n*a^2) <=> a*(sqrt(n)). So, to my question (heh), for the minimum value it's obvious that it would be when n = 0. But I'm a little confused as to what the maximum would be. Say a constant k = a, then would it be k*(sqrt(n))?? Just a simple question I guess, as it comes down to it. Thanks. Actually, wouldn't the min be when n = 1, since there mustb e at least one variable. So the min would be k.