Find maximum value

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Moon
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Find maximum value

Unread post by Moon » Tue Dec 14, 2010 12:32 am

Find the minimum value of $|x - p| + |x - 15| + |x - p - 15|$ for $x$ in the range $p \leq x \leq 15$,
where $ 0 < p < 15$.
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Labib
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Re: Find maximum value

Unread post by Labib » Wed Dec 15, 2010 11:46 pm

I think it's 22. is it correct??
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Moon
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Re: Find maximum value

Unread post by Moon » Thu Dec 16, 2010 12:15 am

Why?
Show us some reason behind your choice. :)
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

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tushar7
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Re: Find maximum value

Unread post by tushar7 » Thu Dec 16, 2010 12:50 am

yap labib you should post the whole solution . and hide it .

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Labib
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Re: Find maximum value

Unread post by Labib » Thu Dec 16, 2010 10:39 pm

I was guessing a bit!! :))
I thought if we assume x=8, p=1 we get the max subs-traction value . so I thought ..... :(
I dont know a better solution method, sorry moon vai n tushar. plz suggest a better method.
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Avik Roy
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Re: Find maximum value

Unread post by Avik Roy » Fri Dec 17, 2010 11:04 am

The trick is to realize that irrespective of the choice of $x$ or $p$, the given expression can be rewritten as:

$(x-p)+(15-x)+(15-(x-p))$

the rest is simple :)
"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor

Muhiminul Maruf
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Re: Find maximum value

Unread post by Muhiminul Maruf » Fri Dec 17, 2010 8:37 pm

i think the minimum value is 15. is it moon vaaia?????? according to avik vaia we get 30- x.........(1)
so, the maximum value of the x will make the lowest value of the equation..... isnt it??????????///
how can i hide it????? and if i hide it, will u be able to see it,moon vaia????????

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Moon
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Re: Find maximum value

Unread post by Moon » Fri Dec 17, 2010 10:35 pm

Yup. :)
Actually the only thing that was necessary to solve this problem was to remember the definition of absolute value. :)
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

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