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

1 Answer
MeneerNask
Jun 22, 2015

Actually there are two derivatives.

Explanation:

As long as #x>=2# the function boils down to #x-2# which has a derivative of #1#.

When #x<=2# the absolute brackets interfere, effectively turning the function into #2-x# which has a derivative of #-1#

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

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