# How do you determine the differentiability of f(x), where #f(x)=|x-1|+|x-2|+|x-3|#?

##### 1 Answer

Dec 8, 2016

Piecewise linear, with different slopes. See the illustrative graph revealing nodes, with double slopes, at x = 1, 2, 3..

#### Explanation:

This is the combined equation for four piecewise definitions.

graph{y-|x-1|-|x-2|-|x-3|=0x^2 [-8.69, 8.685, -4.345, 4.345]}