Write the value of the derivative of `f(x)=|x-1|+|x-3|` at `x=2` .

Options

A. 2
B. 1
C. 0
D. `-2`

Answer

C

Explanation

Let `f(x) = |x-1| +|x-3|`
`={{:(,x-1+x-3, x ge 3),(,x-1+3-x, 1 le x lt 3),(,1-x+3-x, x le 1):}`
`{{:(,2x -4, x ge 3),(,2,1le xle3),(,4-2x, x lt 1):}`
At x = 2 funtion is
`f(x) = 2`
`rArr f(x) = 0`