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

Explanation

We know that ∣x∣=x for all x≥0 and ∣x∣=−x for all x<0. Therefore,
At x=2,

∣x−1∣=x−1 and
∣x−3∣=−(x−3)=−x+3

⇒f(x)=(x−1)+(−x+3)=2

which is a constant function and the derivative of a constant function is always zero.
So at x=2 derivative of f(x) is zero.