x is a real number, attains a minimum at

rengaraj · 2010-01-24T15:10:34+00:00

Sir / Madam, My questions is, The function f(x) = |x – 2| + |2.5 – x| + |3.6 – x|, where x is a real number, attains a minimum at ?? Advance Thanks, R.Rengaraj {InfosysTrain-Q107 Pg26}

x is a real number, attains a minimum at

rengaraj

Member

Updated: Oct 26, 2024

Views: 973

Sir / Madam,
My questions is,

The function f(x) = |x – 2| + |2.5 – x| + |3.6 – x|, where x is a real number, attains a minimum at ??

Advance Thanks,
R.Rengaraj
{InfosysTrain-Q107 Pg26}

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Saandeep Sreerambatla

Member • Jan 24, 2010

Is it 2.9? Notsure though!!

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rengaraj

Member • Jan 25, 2010

Dear English,
Can you explain your answer?
The choices are 2.5,2.7,2.3,None of These
R.Rengaraj

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limestone7000

Member • Jan 27, 2010

my first step would be to club the 2nd and 3rd terms
so,
|2.5 - x| + |3.6 - x|
= |6.1 - 2x|

now,
f(x) = |x - 2| + |6.1 - 2x|

by observing, x shouldn't be negative if u want minimum value of f(x),
so, x>0

now,
for x = 2.3, f(x) = 1.8
for x = 2.5, f(x) = 1.6
for x = 2.7, f(x) = 1.4
[observe that as the value of x increases, value of f(x) decreases]
2.7 could be the answer, but to verify, lets take x = 2.9
so, f(x) = 1.2 for x = 2.9!!!!

hence, the answer is NONE OF THESE!
😀

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rengaraj

Member • Jan 27, 2010

Dear Limestone,
Excellent reply.
Keep it up.
R.Rengaraj

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tdave

Member • Mar 8, 2010

"observe that as the value of x increases, value of f(x) decreases" so x=2.9!

it really take me some time..

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anu_mech

Member • Apr 8, 2010

i suppose u cant club 2.5-x and 3.6-x. 'cause if x is between 2.5 and 3.6 one positive and the other negative
observe the function its value is
f(x)= 8.1-3x (for x<2)
=4.1-x (for 2<x<2.5)
=x-.9 (for 2.5<x<3.6)
=3x-8.1 (for x>3.6)

plot the graph and u get....2.9

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HImanshu_Sharma

Member • Apr 9, 2010

yeah limestone is right

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