Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 230

maximum value

Determine the maximum value of

if

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

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

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

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: maximum value

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