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If b=a+4, then for which of the folloing

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If b=a+4, then for which of the folloing [#permalink] New post 05 Sep 2013, 11:17
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A
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53% (03:02) correct 46% (01:59) wrong based on 45 sessions
If b=a+4, then for which of the following values of x is the expression (x−a)^2+(x−b)^2 the smallest?

A) a−1
B) a
C) a+2
D) a+3
E) a+5

I know that we can solve this question by plugging in the option values. I want to know the smart way to choose which option to plug in first.
[Reveal] Spoiler: OA

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Re: If b=a+4, then for which of the folloing [#permalink] New post 05 Sep 2013, 11:39
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lets take a= 0 ; then b=4 and the equation becomes x^2+(x-4)^2. The minimum value of this function occurs when
x^2 = (x-4)^2 as both of these functions are increasing functions.

Solving this we get x=2 it is minimum. for a=0 option c is gives the value of x as 2.

hope it helps!
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Re: If b=a+4, then for which of the folloing [#permalink] New post 05 Sep 2013, 11:47
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swati007 wrote:
If b=a+4, then for which of the following values of x is the expression (x−a)^2+(x−b)^2 the smallest?

A) a−1
B) a
C) a+2
D) a+3
E) a+5

I know that we can solve this question by plugging in the option values. I want to know the smart way to choose which option to plug in first.


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Re: If b=a+4, then for which of the folloing [#permalink] New post 07 Sep 2013, 05:33
Maxima and minima

Used derivatives here

(x-a)^2+(x-b)^2

First derivative=> 2*(x-a)+2*(x-b) =0 =>x=(a+b)/2 ;substitute b=> x=a+2
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Re: If b=a+4, then for which of the folloing   [#permalink] 07 Sep 2013, 05:33
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