Let `f(x)-|3-|2-|x-1|||, AA x epsilon R` not differentiable at `x_(1),x_(2),x_(3),………………x_(n)`, then `sum_(i=1)^(n)x_(i)^(2)` equal to :

Answer

63

Explanation

`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`