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If f(x)=|x-1|+|x-4| + |x-9|+….+|x-2500| ...

If `f(x)=|x-1|+|x-4| + |x-9|+….+|x-2500| AA x in R`, then all the values of x where f(x) has minimum values lie in

A

(600, 700)

B

(576, 678)

C

(625, 676)

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)=|x-1|+|x+4|+|x-9|+ …. +[x-2500]` is non-differentiable at `x=1^(2), x=2^(2), … , x=50^(2)`.
f(x) is minimum at the middle term of the above series which are `x=25^(2) and x=26^(2)`.
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