Find maximum value
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$.
where $ 0 < p < 15$.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
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Re: Find maximum value
I think it's 22. is it correct??
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Re: Find maximum value
Why?
Show us some reason behind your choice.
Show us some reason behind your choice.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
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Re: Find maximum value
yap labib you should post the whole solution . and hide it .
Re: Find maximum value
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.
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.
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Re: Find maximum value
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
$(x-p)+(15-x)+(15-(x-p))$
the rest is simple
"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor
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Re: Find maximum value
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????????
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????????
Re: Find maximum value
Yup.
Actually the only thing that was necessary to solve this problem was to remember the definition of absolute value.
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.
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.