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The value of (d)/(dx) (|x-1| + |x -5|) a...

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

A

`-2`

B

0

C

2

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
Let ` f(x) = | x -1| + |x - 5|`
`f(x){{:(- (x-1)-(x-5)",",x lt 1),((x-1)-(x-5)"," ,1 le x le 5),(x - 1 + x - 5 ",", x gt 5 ):}`
`f(x){{:(6-2x",",x lt 1),(4"," ,1 le x le 5),(2x - 6 ",", x gt 5 ):}`
Since at ` x = 3 in (1,5)`
` therefore "For" x = 3, f(x) = 4 `
` rArr f'(x) = 0 ` .
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