# How do you differentiate #f(x) = abs(5x-2)#?

##### 2 Answers

This graph has two derivatives, and an undefined one at its corner. The two derivatives are simply the positive and the negative slope, so the graph's right half has a derivative of

Therefore, the two halves meet at

graph{|5x - 2| [-1, 2, -1.215, 4]}

I rewrite it as a piecewise defined function and differentiate each piece.

#### Explanation:

# = {(5x-2," if ",x >= 2/5),(0, " if ", x =2/5),( -5x+2, " if ", x < 2/5):}#

For

For

Because the left and right derivatives are different at

(In fact, there is a corner (cusp) at that point.)