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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:
63
`f(x) = | 3-| 2-| x-1||`
Not differentiable at corner point
` x - 1 = 0 rArr x = 1 " " …..(i)`
`| - 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 bar(pm) , =3 rArr 2 - | x - 1 | = pm 3`
`rArr x - 1 = pm 5 rArr x = 6 , - 4 " "......(iiii)`
From (i) , (ii) &(iii)
` Sum Xi^(2) = 1^(2) + 3^(2) + (-1)^(2) + 6^(2) + (-4)^(2)`
` = 1 + 9 + 1+ 36 + 16`
`sum Xi^(2) = 63`
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