Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2008-07-18 06:39:21

tony123
Member
Registered: 2007-08-03
Posts: 189

### maximum value

Determine the maximum value of

if

Last edited by tony123 (2008-07-18 06:39:53)

Offline

## #2 2008-07-18 07:50:06

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

### Re: maximum value

Obviously we would want

for each i for maximum. Thus, by AMGM,

equality occurring if and only if

.

Togther with

this implies (by symmetry considerations) that
.

Hence

, and

Offline

## #3 2008-07-18 12:49:40

cushydom
Member
Registered: 2008-04-23
Posts: 10

### Re: maximum value

dont know if it makes any difference but you dont need all of the sin(x) to be positive. you could have an even number of them be negative

Offline

## #4 2008-07-20 09:26:37

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

### Re: maximum value

Last edited by JaneFairfax (2008-07-20 11:16:51)

Offline