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Let f (x ) = | 3 - | 2- | x- 1 |||...

Let ` f (x ) = | 3 - | 2- | x- 1 |||, AA x in R ` be not differentiable at ` x _ 1 , x _ 2 , x _ 3, ….x_ n ` , then `sum _ (i= 1 ) ^( n ) x _ i^2 ` equal to :

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The correct Answer is:
C
`f(x)=|3-|2-1|x-1|||`
Not differentiable at corner points
x-1=0 `rArr` x=1 ….(i)
|x-1|=2 `rArr` x-1=`pm`2
`rArr` x=3,-1 ….(ii)
|2-|x-1||=3 `rArr` 2-|x-1|=`pm`3
`rArr` |x-1|=2`pm`3 `rArr` |x-1|=5
`rArr` x-1=`pm`5 x=6,-4 ....(iii)
From (i),(ii),(iii)
`sumXi^2 = 1^2 +3^2 +(-1)^2 + 6^2 +(-4)^2`
=1+9+1+36+16
`sumXi^2`=63
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