Question

Write the value of the derivative of $f\left(x\right)=|x-1|+|x-3|\text{at}x=2.$

Answer 1

for x = 2

$|x-1|=(x-1)\text{and}|x-3|=-(x-3)$

$\frac{d}{dx}(|x-1|+|x-3|)$

$=\frac{d}{dx}(|x-1|)+\frac{d}{dx}(|x-3|)$

$\frac{d}{dx}(x-1)+\frac{d}{dx}(-(x-3\left)\right)$

$\frac{d}{dx}(x-1)+\frac{d}{dx}(3-x)$

$=1-1=0$