# Extra Credit question

1. May 14, 2010

### Metahominid

So I ran into this on my multivariate calculus final this morning, I don't think anyone did it but it has been stuck in my head and I have run out of thoughts.

Let a1, a2, …, an be n positive numbers.
Find the maximum of $$\sum^{n}_{i=1}a_{i}x^_{i}$$subject to the constraint $$\sum^{n}_{i=1}x^{2}_{i} = 1$$

Alright I've never used Latex but I believe that worked. Not quite sure, where to go looks like power sums of power 1,2.

Last edited: May 14, 2010
2. May 14, 2010

### Tedjn

3. May 14, 2010

### Metahominid

Yes, we studied it. About an hour ago I saw the word constraint and it popped into my head but I got discouraged when I tried to formulate it in the terms of functions. I wasn't entirely sure I could say that the summations were functions. I figure I need walk around for a moment and I will see it.

4. May 16, 2010

### darkside00

How do you apply that to the above series though?