How do you find the derivative of abs(x-2)?

1 Answer
Jun 22, 2015

Actually there are two derivatives.

Explanation:

As long as $x \ge 2$ the function boils down to $x - 2$ which has a derivative of $1$.

When $x \le 2$ the absolute brackets interfere, effectively turning the function into $2 - x$ which has a derivative of $- 1$

At the point $\left(2 , 0\right)$ the derivative could be either, depending on what side you approach it from.
graph{|x-2| [-7, 13, -2.4, 7.6]}