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priyankagumber: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Thu Aug 16, 2007 6:45 am

functions

by priyankagumber » Wed Jul 22, 2009 8:42 am

Find the minimum value of the following function:
f(x) = (x – 5)2 + (x – 7)2 – (x – 4)2 – (x – 8)2 + (x – 3)2 + (x – 9)2

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Source: Beat The GMAT — Problem Solving | Wed Jul 22, 2009 8:42 am

ketkoag: Legendary Member; Posts: 876; Joined: Thu Apr 10, 2008 8:14 am; Thanked: 13 times

Re: functions

by ketkoag » Wed Jul 22, 2009 1:04 pm

priyankagumber wrote:Find the minimum value of the following function:
f(x) = (x – 5)2 + (x – 7)2 – (x – 4)2 – (x – 8)2 + (x – 3)2 + (x – 9)2

IMO minimum value is 4.

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real2008: Legendary Member; Posts: 527; Joined: Thu May 01, 2008 12:06 am; Thanked: 7 times

Re: functions

by real2008 » Thu Jul 23, 2009 2:42 am

priyankagumber wrote:Find the minimum value of the following function:
f(x) = (x – 5)2 + (x – 7)2 – (x – 4)2 – (x – 8)2 + (x – 3)2 + (x – 9)2

pl. confirm that question is rightly typed or not?
I have doubt whether (x-5)2 is (x-5)*2 or (x-5)^2 and so on...

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raghavsarathy: Master | Next Rank: 500 Posts; Posts: 166; Joined: Sat Apr 18, 2009 10:41 pm; Thanked: 9 times; GMAT Score:770

by raghavsarathy » Thu Jul 23, 2009 5:35 am

(x – 5)2 + (x – 7)2 – (x – 4)2 – (x – 8)2 + (x – 3)2 + (x – 9)2

Expanding the eqn

2x - 10 + 2x - 14 -2x +8 - 2x + 16 + 2x - 6 + 2x - 18

solving this we will end up with
4x - 24

A minumum value for this will depend on the value of x

x can extend upto -infinity.

I think in the question it must be square of..

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800