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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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#1 2008-07-19 04:39:21

tony123
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maximum value

Determine the maximum value of




if

Last edited by tony123 (2008-07-19 04:39:53)

 

#2 2008-07-19 05:50:06

JaneFairfax
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Re: maximum value

Obviously we would want

for each i for maximum. Thus, by AMGM,



equality occurring if and only if
.

Togther with
this implies (by symmetry considerations) that
.

Hence
, and


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

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#3 2008-07-19 10:49:40

cushydom
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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

 

#4 2008-07-21 07:26:37

JaneFairfax
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Re: maximum value

Last edited by JaneFairfax (2008-07-21 09:16:51)


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.
 

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