The value of `(d)/(dx) (|x-1| + |x -5|)` at x = 3 is

Options

A. `-2`
B. 0
C. 2
D. 4

Answer

B

Explanation

Let `f(x) = |x-1| + |x-5|`
`f(x) = {:{(-(x-1)-(x-5),, xlt1),((x-1)-(x-5),, 1lex le5),(x-1+x-5,,xlt5):}`
`f(x) = {:{(6-2x",",,xle1),(4",",,1lexle5),(2x-6",",,xgt5):}`
`because x = 3 in [1, 5]`
`therefore " For" x = 3`
`(x) = 4 rArr f'(x) = 0`